{"id":43699,"date":"2023-02-03T10:00:16","date_gmt":"2023-02-03T04:30:16","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=43699"},"modified":"2023-02-03T10:03:59","modified_gmt":"2023-02-03T04:33:59","slug":"ml-aggarwal-class-6-solutions-for-icse-maths-chapter-13-ex-13-1","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/ml-aggarwal-class-6-solutions-for-icse-maths-chapter-13-ex-13-1\/","title":{"rendered":"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry"},"content":{"rendered":"<h2>ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Objective Type Questions<\/h2>\n<p><strong>Mental Maths<\/strong><br \/>\nQuestion 1.<br \/>\nFill in the blanks:<br \/>\n(i) A ruler is used to draw line and to measure their &#8230;&#8230;&#8230;&#8230;<br \/>\n(ii) A divider is sued to compare &#8230;&#8230;&#8230;&#8230;<br \/>\n(iii) A compass is used to draw circles or arcs of &#8230;&#8230;&#8230;&#8230;<br \/>\n(iv) A protractor is used to draw and measure &#8230;&#8230;&#8230;&#8230;<br \/>\n(v) The set squares are two triangular pieces having angles of &#8230;&#8230;&#8230;&#8230; and &#8230;&#8230;&#8230;&#8230;<br \/>\n(vi) To bisect a line segment of length 7 cm, the opening of the&#8217; compass should be more than &#8230;&#8230;&#8230;&#8230;<br \/>\n(vii) The perpendicular bisector of a line segment is also its line of &#8230;&#8230;&#8230;&#8230;<br \/>\nSolution:<br \/>\n(i) A ruler is used to draw line segments and to measure their lengths.<br \/>\n(ii) A divider is sued to compare lengths of line segment.<br \/>\n(iii) A compass is used to draw circles or arcs of circles.<br \/>\n(iv) A protractor is used to draw and measure angles.<br \/>\n(v) The set squares are two triangular pieces having angles of<br \/>\n30\u00b0, 60\u00b0, 90\u00b0 and 45\u00b0, 45\u00b0, 90\u00b0.<br \/>\n(vi) To bisect a line segment of length 7 cm,<br \/>\nthe opening of the compass should be more than 3.5 cm.<br \/>\n(vii) The perpendicular bisector of a line segment is also its line of symmetry.<\/p>\n<p>Question 2.<br \/>\nState whether the following statements are true (T) or false (F):<br \/>\n(i) There is only one set square in a geometry box.<br \/>\n(ii) An angle can be copied with the help of a ruler and compass.<br \/>\n(iii) The perpendicular bisector of a line segment can be drawn by paper folding.<br \/>\n(iv) Perpendicular to a line from a given point not on it can be drawn by paper folding.<br \/>\n(v) A 45\u00b0 &#8211; 45\u00b0 &#8211; 90\u00b0 set square and a protractor have the same number of line(s) of symmetry.<br \/>\nSolution:<br \/>\n(i) There is only one set square in a geometry box. False<br \/>\n(ii) An angle can be copied with the help of a ruler and compass. True<br \/>\n(iii) The perpendicular bisector of a line segment<br \/>\ncan be drawn by paper folding. True<br \/>\n(iv) Perpendicular to a line from a given point not on it<br \/>\ncan be drawn by paper folding. True<br \/>\n(v) A 45\u00b0 &#8211; 45\u00b0 &#8211; 90\u00b0 set square and a protractor have<br \/>\nthe same number of line(s) of symmetry. True<\/p>\n<p><strong>Multiple Choice Questions<\/strong><br \/>\n<strong>Choose the correct answer from the given four options (3 to 13):<\/strong><br \/>\nQuestion 3.<br \/>\nA circle of any radius can be constructed with the help of a:<br \/>\n(a) ruler<br \/>\n(b) divider<br \/>\n(c) compass<br \/>\n(d) protractor<br \/>\nSolution:<br \/>\ncompass (c)<\/p>\n<p>Question 4.<br \/>\nThe instrument in a geometry box having the shape of a semicircle is :<br \/>\n(a) ruler<br \/>\n(b) divider<br \/>\n(c) compass<br \/>\n(d) protractor<br \/>\nSolution:<br \/>\nprotractor (d)<br \/>\nIt is used to draw or measure angles.<\/p>\n<p>Question 5.<br \/>\nThe instrument to measure an angle is<br \/>\n(a) ruler<br \/>\n(b) protractor.<br \/>\n(c) divider<br \/>\n(d) compass<br \/>\nSolution:<br \/>\nprotractor (b)<\/p>\n<p>Question 6.<br \/>\nWhich of the following angles cannot be constructed using ruler and compas?<br \/>\n(a) 15\u00b0<br \/>\n(b) 45\u00b0<br \/>\n(c) 75\u00b0<br \/>\n(d) 85\u00b0<br \/>\nSolution:<br \/>\n85\u00b0 (d)<\/p>\n<p>Question 7.<br \/>\nThe number of perpendiculars that can be drawn to a line from a point not on it is<br \/>\n(a) 1<br \/>\n(b) 2<br \/>\n(c) 4<br \/>\n(d) infinitely many<br \/>\nSolution:<br \/>\n1 (a)<\/p>\n<p>Question 8.<br \/>\nThe number of perpendicular bisectors that can be drawn of a given line segment is :<br \/>\n(a) 0<br \/>\n(b) 1<br \/>\n(c) 2<br \/>\n(d) infinitely many<br \/>\nSolution:<br \/>\n1 (b)<\/p>\n<p>Question 9.<br \/>\nThe number of lines of symmetry in a picture of a divider is:The number of lines of symmetry in a picture of compass is<br \/>\n(a) 0<br \/>\n(b) 1<br \/>\n(c) 2<br \/>\n(d) 4<br \/>\nSolution:<br \/>\n1 (b)<\/p>\n<p>Question 10.<br \/>\nThe number of lines of symmetry in a picture of compass is<br \/>\n(a) 0<br \/>\n(b) 1<br \/>\n(c) 2<br \/>\n(d) none of these<br \/>\nSolution:<br \/>\n0 (a)<\/p>\n<p>Question 11.<br \/>\nThe number of lines of symmetry in a ruler is<br \/>\n(a) 0<br \/>\n(b) 1<br \/>\n(c) 2<br \/>\n(d) 4<br \/>\nSolution:<br \/>\n2 (c)<\/p>\n<p>Question 12.<br \/>\nThe number of lines of symmetry in a 30\u00b0 &#8211; 60\u00b0 &#8211; 90\u00b0 set square is<br \/>\n(a) 0<br \/>\n(b) 1<br \/>\n(c) 2<br \/>\n(d) 3<br \/>\nSolution:<br \/>\n0 (a)<\/p>\n<p>Question 13.<br \/>\nThe number of lines of symmetry in a protractor is<br \/>\n(a) 0<br \/>\n(b) 1<br \/>\n(c) 2<br \/>\n(d) more than 2<br \/>\nSolution:<br \/>\n1 (b)<\/p>\n<h2>ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Check Your Progress<\/h2>\n<p>Question 1.<br \/>\nDraw a line segment AB = 5.4 cm. Construct a perpendicular at A by using ruler and compass.<br \/>\nSolution:<br \/>\nSteps of construction:<\/p>\n<ol>\n<li>Draw AB = 5.4 cm.<\/li>\n<li>With any radius draw an arc which cuts AB at M.<\/li>\n<li>With M as centre and the same radius<br \/>\ncut the previous arc at N and P.<\/li>\n<li>With N and P as centres draw arcs which intersect at L.<br \/>\nJoin AL.<\/li>\n<li>AL is required perpendicular.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80552\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Check-Your-Progress-1.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Check Your Progress 1\" width=\"233\" height=\"196\" \/><\/li>\n<\/ol>\n<p>Question 2.<br \/>\nDraw a line segment PQ = 6.8 cm. Draw a perpendicular to it from a point A outside PQ by using ruler and compass.<br \/>\nSolution:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80553\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Check-Your-Progress-2.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Check Your Progress 2\" width=\"200\" height=\"243\" \/><br \/>\nSteps of construction:<\/p>\n<ol>\n<li>Draw a line segment PQ = 6.8 cm<br \/>\nand take a point A outside PQ.<\/li>\n<li>With A as centre and any suitable radius,<br \/>\ndraw an arc to cut line PQ at point C and D.<\/li>\n<li>With C and D as centres,<br \/>\ndraw two arcs of equal radius cutting each other<br \/>\nat B on the other side of line PQ.<\/li>\n<li>Join AB to meet the line PQ at M.<\/li>\n<\/ol>\n<p>Question 3.<br \/>\nDraw a line segment of length 6.5 cm and construct its axis of symmetry.<br \/>\nSolution:<br \/>\nSteps of construction:<\/p>\n<ol>\n<li>Draw a line segment \\(\\overline{\\mathrm{AB}}\\) of length 6.5 cm.<\/li>\n<li>With A as centre, using a compass, draw a circle.<br \/>\nThe radius of this circle should be more than half of the length of \\(\\overline{\\mathrm{AB}}\\).<\/li>\n<li>With the same radius and with B as centre,<br \/>\ndraw another circle using a compass.<br \/>\nLet it cut the previous circle at C and D.<\/li>\n<li>Join CD. Then, \\(\\overline{\\mathrm{CD}}\\) is the axis of symmetry of \\(\\overline{\\mathrm{AB}}\\).<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80554\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Check-Your-Progress-3.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Check Your Progress 3\" width=\"326\" height=\"250\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Check-Your-Progress-3.png 326w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Check-Your-Progress-3-300x230.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><\/li>\n<\/ol>\n<p>Question 4.<br \/>\nDraw \u2220AOB = 76\u00b0 with help of a protractor. Bisect this angle by using ruler and compass. Measure the two parts by your protractor and see how accurate you are.<br \/>\nSolution:<br \/>\nSteps of construction:<\/p>\n<ol>\n<li>Draw a line segment OB.<\/li>\n<li>Construct \u2220AOB with the help of protector = 76\u00b0.<\/li>\n<li>With the help of compass and O as centre<br \/>\ndraw an arc meeting OB and OA at P and Q respectively.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80555\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Check-Your-Progress-4.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Check Your Progress 4\" width=\"176\" height=\"195\" \/><\/li>\n<li>With P and Q as centre and radius more than \\(\\frac{1}{2}\\) PQ<br \/>\ndraw two arcs meeting each other at R.<\/li>\n<li>OD is the bisector of \u2220AOB.<\/li>\n<li>On measuring \u2220AOD = \u2220DOB = 38\u00b0.<\/li>\n<\/ol>\n<p>Question 5.<br \/>\nBy using and compass, construct an angle of 135\u00b0 and bisect it. Measure any one part by protractor and see how accurate you are.<br \/>\nSolution:<br \/>\nSteps of construction:<\/p>\n<ol>\n<li>Draw a line OB with help of ruler.<\/li>\n<li>With O as a centre and any suitable radius<br \/>\ndraw an arc to meet OB at S.<\/li>\n<li>With S as a centre and same radius<br \/>\ndraw an arc to meet the previous arc at L.<br \/>\nWith L as centre and same radius\u00a0draw another arc M.<br \/>\nAgain M as centre draws another arc to meet the first arc at N.<\/li>\n<li>With M and N as centres draw two arcs of<br \/>\nequal radius \\(\\left(&gt;\\frac{1}{2} \\mathrm{SL}\\right)\\) cutting each other at A.<\/li>\n<li>Join OA intersecting the radius at point Q.<\/li>\n<li>Now taking Q and M as a centres<br \/>\ndraw two arcs of equal radius cutting each other at P.<\/li>\n<li>Join PO.<\/li>\n<li>Measuring the \u2220POB with protractor we get \u2220POB equal to 135\u00b0.<\/li>\n<li>Taking S and R as a centres draw two arcs cutting each other at T.<br \/>\nJoin TO.<\/li>\n<li>\u2220TOB is the bisector of \u2220POB. \u2220TOB = \u2220TOP = 67.5\u00b0.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80557\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Check-Your-Progress-5.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Check Your Progress 5\" width=\"299\" height=\"144\" \/><\/li>\n<\/ol>\n<h2>ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1<\/h2>\n<p>Question 1.<br \/>\nConstruct a circle of radius:<br \/>\n(i) 2 cm<br \/>\n(ii) 3.5 cm<br \/>\nSolution:<br \/>\n(a) 2 cm<br \/>\nSteps of construction :<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80520\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-1.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1 1\" width=\"219\" height=\"209\" \/><br \/>\n(i) Open the compasses for the required radius 2 cm,<br \/>\nby putting the pointer on 0 and opening the pencil up to 2 cm<br \/>\n(ii) Draw a point with a sharp pencil and marks it as Q in the centre.<br \/>\n(iii) Place the pointer of the compasses where the centre has been marked.<br \/>\n(iv) Turn the compasses slowly to draw the circle.<\/p>\n<p>(b) 3.5 cm<br \/>\nSteps of construction :<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80521\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-2.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1 2\" width=\"237\" height=\"238\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-2.png 237w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-2-150x150.png 150w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-2-100x100.png 100w\" sizes=\"(max-width: 237px) 100vw, 237px\" \/><br \/>\n(i) Open the compasses for the required radius 3.5cm<br \/>\nputting the pointer on 0 and openin&#8217; g the pencil up to 3.5 cm<br \/>\n(ii) Draw a Point with a share Pencil and marks it as O in the centre.<br \/>\n(iii) Place the pointer of the compasses where the centre has been marked.<br \/>\n(iv) Turn the compasses slowly to draw the circle.<\/p>\n<p>Question 2.<br \/>\nWith the same centre O, draw two circles of radii 2.6 cm and 4.1 cm.<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(a) For a circle of radius 4.1 cm<br \/>\n(i) Pen the cor.npasses for the required radius 4.1 cm,<br \/>\nby putting the pointer on 0 and opening the pencil up to 4.1 cm.<br \/>\n(ii) Place the pointer of the compasses at 0.<br \/>\n(iii) Turn the compasses slowly t0 draw the circle.<\/p>\n<p>(b) For a circle of radius of 2.6 cm<br \/>\n(i) Open the compasses for the required radius 2.6 cm,<br \/>\nby putting the pointer on 0 and opening the pencil up to 2.6 cm.<br \/>\n(ii) Place the pointer of the compasses at O.<br \/>\n(iii) Turn the compasses slowly to draw the circle.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80522\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-3.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1 3\" width=\"276\" height=\"275\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-3.png 276w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-3-150x150.png 150w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-3-100x100.png 100w\" sizes=\"(max-width: 276px) 100vw, 276px\" \/><\/p>\n<p>Question 3.<br \/>\nDraw any circle and mark points A, B and C such that<br \/>\n(i) A is on the circle.<br \/>\n(ii) B is in the interior of the circle.<br \/>\n(iii) C is in the exterior of the circle.<br \/>\nSolution:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80523\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-4.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1 4\" width=\"697\" height=\"474\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-4.png 697w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-4-300x204.png 300w\" sizes=\"(max-width: 697px) 100vw, 697px\" \/><\/p>\n<p>Question 4.<br \/>\nDraw a circle and any two of its (non-perpendicular) diameters. If you join the ends of these diameters, what is the figure obtained? What figure is obtained if the diameters are perpendicular to each other? How do you check your answer?<br \/>\nSolution:<br \/>\n(i) On joining the ends of any two diameters of the circle,<br \/>\nthe figure obtained is a rectangle.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80525\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-5.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1 5\" width=\"215\" height=\"213\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-5.png 215w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-5-150x150.png 150w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-5-100x100.png 100w\" sizes=\"(max-width: 215px) 100vw, 215px\" \/><br \/>\n(ii) On joining the ends of any two diameters of the circle,<br \/>\nperpendicular to each other, the figure obtained is a square.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80526\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-6.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1 6\" width=\"215\" height=\"210\" \/><br \/>\nTo check the answer,<br \/>\nwe measured the sides and angles of the figure obtained.<\/p>\n<p>Question 5.<br \/>\nLet A, B be the centres of two circles of equal radii; draw them so that each one of them passes through the centre of the other. Let them intersect at C and D.<br \/>\nExamine whether \\(\\overline{\\mathrm{AB}}\\) and \\(\\overline{\\mathrm{CD}}\\) are at right angles.<br \/>\nSolution:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80527\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-7.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1 7\" width=\"314\" height=\"215\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-7.png 314w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-7-300x205.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nYes! \\(\\overline{\\mathrm{AB}}\\) and \\(\\overline{\\mathrm{CD}}\\) are at right angles.<\/p>\n<p>Question 6.<br \/>\nConstruct a line segment of length of 6.3 cm using ruler and compass.<br \/>\nSolution:<br \/>\nUsing ruler, we mark two points A and B which are 7.3 cm apart.<br \/>\nJoin A and B and get AB.<br \/>\n\\(\\overline{\\mathrm{AB}}\\) is a line segment of length 7.3 cm<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80528\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-8.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1 8\" width=\"269\" height=\"34\" \/><\/p>\n<p>Question 7.<br \/>\nConstruct \\(\\overline{\\mathrm{AB}}\\) of length 8.3 cm. From this cut off \\(\\overline{\\mathrm{AC}}\\) of length 5.6 cm. Measure the length of BC . .<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(i) Draw a line l. Mark a point A on line l.<br \/>\n(ii) Place the compass pointer on the zero mark of the ruler.<br \/>\nOpen it to place the pencil point upto the 8.3 cm mark.<br \/>\n(iii) Without changing the opening of the compass,<br \/>\nplace the pointer on A and swing an arc to cut l at B.<br \/>\n(iv) \\(\\overline{\\mathrm{AB}}\\) is a line segment of required of length 8.3 cm.<br \/>\n(v) Place the compass pointer on the zero mark of the ruler.<br \/>\nOpen it to place the pencil point upto 5.6 cm mark.<br \/>\n(vi) Withtout changing the opening of the compass,<br \/>\nplace the pointer on A and swing ana rc to cut l at C.<br \/>\n(vii) \\(\\overline{\\mathrm{AC}}\\) is a line segment of length 5.6 cm.<br \/>\nOn measurement, \\(\\overline{\\mathrm{BC}}\\) = 2.7 cm.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80529\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-9.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1 9\" width=\"234\" height=\"152\" \/><\/p>\n<p>Question 8.<br \/>\nDraw any line segment \\(\\overline{\\mathrm{PQ}}\\). Without measure \\(\\overline{\\mathrm{PQ}}\\), construct a copy of \\(\\overline{\\mathrm{PQ}}\\).<br \/>\nSolution:<br \/>\n(i) Given \\(\\overline{\\mathrm{PQ}}\\) whose length is not known.<br \/>\n(ii) Fix the compass pointer on P and the pencil end on Q.<br \/>\nThe opening of the instrument now gives the length of \\(\\overline{\\mathrm{PQ}}\\).<br \/>\n(iii) Draw any line l. Choose a point A on l.<br \/>\nWithout changing the compass setting, place the pointer on A.<br \/>\n(iv) Swing an arc that cuts l at a point, say, B. Now AB is a copy of \\(\\overline{\\mathrm{PQ}}\\).<\/p>\n<p>Question 9.<br \/>\nGiven some line segment \\(\\overline{\\mathrm{AB}}\\), whose length you do not know, construct \\(\\overline{\\mathrm{PQ}}\\) such that the length of \\(\\overline{\\mathrm{PQ}}\\) is twice that of \\(\\overline{\\mathrm{AB}}\\).<br \/>\nSolution:<br \/>\n(i) Given \\(\\overline{\\mathrm{AB}}\\) whose length is not known.<br \/>\n(ii) Fix the compass pointer on A and the pencil end on B.<br \/>\nThe opening of the instrument now gives the length of AB.<br \/>\n(iii) Draw any line 1. Choose a point P on l.<br \/>\nWithout changing the compass setting, place the pointer on P.<br \/>\n(iv) Strike an arc that cuts l at a point, say, X.<br \/>\n(v) Now fix the compass pointer on X.<br \/>\nStrike an arc away from P that cuts l at a point, say, Q.<br \/>\nNow, the length of \\(\\overline{\\mathrm{PQ}}\\) is twice that of AB.<\/p>\n<p>Question 10.<br \/>\nTake a line segment \\(\\overline{\\mathrm{PQ}}\\) of length 10 cm. From \\(\\overline{\\mathrm{PQ}}\\), cut of \\(\\overline{\\mathrm{PA}}\\) of length 4.3 cm and \\(\\overline{\\mathrm{BQ}}\\) of length 2.5 cm. Measure the length of segment \\(\\overline{\\mathrm{AB}}\\).<br \/>\nSolution:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80530\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-10.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1 10\" width=\"276\" height=\"80\" \/><br \/>\n\u2234 Length of \\(\\overline{\\mathrm{AB}}\\) is 3.2 cm.<\/p>\n<p>Question 11.<br \/>\nGiven two line segments \\(\\overline{\\mathrm{AB}}\\) and \\(\\overline{\\mathrm{CD}}\\) of length 7.5 cm and 4.6 respectively. Construct line segments.<br \/>\n(i) \\(\\overrightarrow { PQ } \\) of length equal to the sum of the lengths of \\(\\overline{\\mathrm{AB}}\\) and \\(\\overline{\\mathrm{CD}}\\).<br \/>\n(ii) \\(\\overline{\\mathrm{XY}}\\) of length equal to the difference of the lengths of \\(\\overline{\\mathrm{AB}}\\) and \\(\\overline{\\mathrm{CD}}\\). Verify these lengths by measurements.<br \/>\nSolution:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80531\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.1-11.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1 11\" width=\"300\" height=\"164\" \/><br \/>\n(ii) \\(\\overline{\\mathrm{XY}}\\) = \\(\\overline{\\mathrm{AB}}\\) &#8211; \\(\\overline{\\mathrm{CD}}\\) = 7.5 cm &#8211; 4.6 cm = 2.9 cm<\/p>\n<h2>ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.2<\/h2>\n<p>Question 1.<br \/>\nDraw a line segment \\(\\overline{\\mathrm{PQ}}\\) =5.6 cm. Draw a perpendicular to it from a point A outside \\(\\overline{\\mathrm{PQ}}\\) by using ruler and compass.<br \/>\nSolution:<br \/>\nGiven: A-Line segment PQ = 5.6 cm and a point A outside the line.<br \/>\nRequired: To draw a 1 ar to PQ from point A.<br \/>\nSteps of construction :<br \/>\n(i) With A as centre and any suitable radius,<br \/>\ndrawn an arc to cut the line PQ at points C and D.<br \/>\n(ii) With C and D as centres, drawn two arcs of equal radius \\(\\left(&gt;\\frac{1}{2} \\mathrm{CD}\\right)\\)<br \/>\ncutting each other at B on the other side of PQ.<br \/>\n(iii) Join A and B to meet the line PQ at N,<br \/>\nthen AN is the required perpendicular from the point A to the line PQ.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80533\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-1.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.2 1\" width=\"197\" height=\"255\" \/><\/p>\n<p>Question 2.<br \/>\nDraw a line segment \\(\\overline{\\mathrm{AB}}\\) = 6.2 cm. Draw a perpendicular to it at a point M on \\(\\overline{\\mathrm{AB}}\\) by using ruler and compass.<br \/>\nSolution:<br \/>\nGiven: A line AB = 6.2 cm and a point P on it.<br \/>\nRequired: To draw an \u22a5 arc to AB at point P.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80534\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-2.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.2 2\" width=\"198\" height=\"236\" \/><br \/>\nStep of Construction :<br \/>\n(i) With P as centre and any suitable radius,<br \/>\ndraw an arc to cut the line AB at points C and D.<br \/>\n(ii) With C and D as centres,<br \/>\ndraw two arcs of equal radius \\(\\left(&gt;\\frac{1}{2} \\mathrm{CD}\\right)\\) cutting each other at Q.<br \/>\n(iii) Join P and Q.<br \/>\nthen QP is the required perpendicular to the line AB at the point P.<\/p>\n<p>Question 3.<br \/>\nDraw a line l and take a point P on it. Through P, draw a line segment \\(\\overline{\\mathrm{PQ}}\\) perpendicular to l. Now draw a perpendicular to \\(\\overline{\\mathrm{PQ}}\\) at Q (use ruler and compass).<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(i) Let AB be the given line segment.<br \/>\n(ii) With A as centre and any suitable radius \\(\\left(&gt;\\frac{1}{2} \\mathrm{CD}\\right)\\)<br \/>\ndraw arcs on each side of AB.<br \/>\n(iii) With B as centre and same radius [as in step (i)],<br \/>\ndraw arcs on each side of AB to cut the previous arcs at P and Q.<br \/>\n(iv) Draw a line passing through points P and Q,<br \/>\nthen the lines \\(\\overline{\\mathrm{PQ}}\\) is the required perpendicular bisector of AB and line l.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80535\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-3.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.2 3\" width=\"217\" height=\"214\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-3.png 217w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-3-100x100.png 100w\" sizes=\"(max-width: 217px) 100vw, 217px\" \/><\/p>\n<p>Question 4.<br \/>\nDraw a line segment \\(\\overline{\\mathrm{AB}}\\) of length 6.4 cm and construct its axis of symmetry (use ruler and compass).<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(i) Draw a line segment \\(\\overline{\\mathrm{AB}}\\) of length 6.4 cm.<br \/>\n(ii) With A as centre, using a compass, draw a circle.<br \/>\nThe radius of this circle should be more than half of the length of AB.<br \/>\n(iii) With the same radius and with B as centre,<br \/>\ndraw another circle using a compass.<br \/>\nLet it cut the previous circle at C and D.<br \/>\n(iv) Join \\(\\overline{\\mathrm{CD}}\\). Then, \\(\\overline{\\mathrm{CD}}\\) is the axis of symmetry of \\(\\overline{\\mathrm{AB}}\\).<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80536\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-4.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.2 4\" width=\"322\" height=\"253\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-4.png 322w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-4-300x236.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><\/p>\n<p>Question 5.<br \/>\nDraw the perpendicular bisector of \\(\\overline{\\mathrm{XY}}\\) whose length is 8.3 cm.<br \/>\n(i) Take any point P on the bisector drawn. Examine whether PX = PY.<br \/>\n(ii) If M is the mid-point of \\(\\overline{\\mathrm{XY}}\\), what can you say about the lengths MX and MY?<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(i) Draw a line segment \\(\\overline{\\mathrm{XY}}\\) of length 8.3 cm.<br \/>\n(ii) With X as centre, using compass, draw a circle.<br \/>\nThe radius of this circle should be more than half of the length of \\(\\overline{\\mathrm{XY}}\\).<br \/>\n(iii) With the same radius and with Y as centre,<br \/>\ndraw another circle using a compass.<br \/>\nLet it cut the previous circle at A and B.<br \/>\n(iv) Join AB.<br \/>\nThen, \\(\\overline{\\mathrm{AB}}\\) is the perpendicular bisector of the line segment \\(\\overline{\\mathrm{XY}}\\).<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80538\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-5.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.2 5\" width=\"259\" height=\"280\" \/><br \/>\n(a) On examination, we find the PX = PY.<br \/>\n(b) We can say that the length of MX is Equal to the length of MY.<\/p>\n<p>Question 6.<br \/>\nDraw a line segment of length 8.8 cm. Using ruler and compass, divide it into four equal parts. Verify by actual measurement.<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(i) Draw a line segment \\(\\overline{\\mathrm{AB}}\\) of length 8.8 cm.<br \/>\n(ii) With A as centre, using compass,<br \/>\ndraw two arcs on either side of AB.<br \/>\nThe radius of this arc should be more than half of the length of \\(\\overline{\\mathrm{AB}}\\).<br \/>\n(iii) With the same radius and with B as ctntre,<br \/>\ndraw another arc using compass.<br \/>\nLet it cut the previous arc at C and D.<br \/>\n(iv) Join \\(\\overline{\\mathrm{CD}}\\).<br \/>\nIt cuts \\(\\overline{\\mathrm{AB}}\\) at E.<br \/>\nThen \\(\\overline{\\mathrm{CD}}\\) is the perpendicular bisector of the line segment \\(\\overline{\\mathrm{AB}}\\).<br \/>\n(v) With A as centre, using compass, draw a circle.<br \/>\nThe radius of this circle stould be more than half of the length of Ac.<br \/>\n(vi) With the same radius and with E as ceitre,<br \/>\ndraw another circle using compass.<br \/>\nLet it cut the previous circle at F ana G.<br \/>\n(vii) Join \\(\\overline{\\mathrm{FG}}\\) . It cuts \\(\\overline{\\mathrm{AE}}\\) at H.<br \/>\nThen \\(\\overline{\\mathrm{FG}}\\) is the perpendicular bisector of the line segment \\(\\overline{\\mathrm{AE}}\\).<br \/>\n(viii) With E as centre, using eompass, draw a circle.<br \/>\nThe radius of thii circle slould be more than half of the length of EB.<br \/>\n(ix) With the same radius md with B is centre,<br \/>\ndraw another circle using compss.<br \/>\nLet it cut the previous cirde at I and J.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80539\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-6.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.2 6\" width=\"340\" height=\"272\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-6.png 340w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-6-300x240.png 300w\" sizes=\"(max-width: 340px) 100vw, 340px\" \/><br \/>\n(x) Join \\(\\overline{\\mathrm{IJ}}\\) . It cuts \\(\\overline{\\mathrm{EB}}\\) at K.<br \/>\nThen \\(\\overline{\\mathrm{IJ}}\\) is the perpendicuir bisector of the lhe segment \\(\\overline{\\mathrm{EB}}\\).<br \/>\nNow, the points H, E and K divide AB into four equal parts. i. e.,<br \/>\n\\(\\overline{\\mathrm{AH}}\\) = \\(\\overline{\\mathrm{HE}}\\) = \\(\\overline{\\mathrm{EK}}\\) = \\(\\overline{\\mathrm{KB}}\\)<br \/>\nBy measurement,<br \/>\n\\(\\overline{\\mathrm{AH}}\\) = \\(\\overline{\\mathrm{HE}}\\) = \\(\\overline{\\mathrm{EK}}\\) = \\(\\overline{\\mathrm{KB}}\\) = 2.2 cm<\/p>\n<p>Question 7.<br \/>\nWith \\(\\overline{\\mathrm{PQ}}\\) of length 5.6 cm as diameter, draw a circle.<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(i) Draw a line segment \\(\\overline{\\mathrm{PQ}}\\) of length 5.6 cm.<br \/>\n(ii) With P as centre, using compass, draw a circle.<br \/>\nThe radius of this circle should be more than half of the length of \\(\\overline{\\mathrm{PQ}}\\).<br \/>\n(iii) With the same radius and with Q as centre,<br \/>\ndraw another circle using compass.<br \/>\nLet it cut the previous circle at A and B.<br \/>\n(iv) Join \\(\\overline{\\mathrm{AB}}\\). It cuts \\(\\overline{\\mathrm{PQ}}\\) at C.<br \/>\nThen AB is the perpendicular bisector of the line segment \\(\\overline{\\mathrm{PQ}}\\).<br \/>\n(v) Place the pointer of the compass at C<br \/>\nand open the pencil up to P.<br \/>\n(vi) Turn the compass slowly to draw the circle.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80540\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-7.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.2 7\" width=\"235\" height=\"292\" \/><\/p>\n<p>Question 8.<br \/>\nDraw a circle with centre C and radius 4.2 cm. Draw any chord AB. Construct the perpendicular bisector of AB and examine if it passes through C.<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(i) Draw a point with a sharp pencil aid mark it as C.<br \/>\n(ii) Open the compass for the required radius of 4.2 cm,<br \/>\nby putting the pointer on 0 and opening the pencil up to 4.2 cm.<br \/>\n(iii) Place the pointer of the compass at C.<br \/>\n(iv) Turn the compass slowly to draw the circle.<br \/>\n(v) Draw any chord \\(\\overline{\\mathrm{AB}}\\) of this circle.<br \/>\n(vi) With A as centre, using compass, draw a circle.<br \/>\nThe radius of this circle should be more than half of the length of \\(\\overline{\\mathrm{AB}}\\).<br \/>\n(vii) With the same radius and with B as centre,<br \/>\ndraw another circle using compass.<br \/>\nLet it cut the previous circle at D and E.<br \/>\n(viii) Join \\(\\overline{\\mathrm{DE}}\\).<br \/>\nThen \\(\\overline{\\mathrm{DE}}\\) is the perpendicular bisector of the line segment \\(\\overline{\\mathrm{AB}}\\).<br \/>\nOn examination, we find that it passes through C.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80541\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-8.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.2 8\" width=\"234\" height=\"217\" \/><\/p>\n<p>Question 9.<br \/>\nDraw a circle of radius 3.5 cm. Draw any two of its (non-parallel) chords. Construct the perpendicular bisectors of these chords. Where do they meet?<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(i) Draw a point with a sharp pencil and mark it as O.<br \/>\n(ii) Open the compasses for the required radius 3.5 cm,<br \/>\nby putting the pointer on 0 and opening the pencil upto 3.5 cm.<br \/>\n(iii) Place the pointer of the compass at O.<br \/>\n(iv) Turn the compass slowly to draw the circle.<br \/>\n(v) Draw any two chords \\(\\overline{\\mathrm{AB}}\\)B and \\(\\overline{\\mathrm{CD}}\\) of this circle.<br \/>\n(vi) With A as centre, using compass, draw two arcs on either side of AB.<br \/>\nThe radius of this arc should be more than half of the length of \\(\\overline{\\mathrm{AB}}\\).<br \/>\n(vii) With the same radius and with B as centre,<br \/>\ndraw another two arcs using compass.<br \/>\nLet it cut the previous circle at E and F.<br \/>\n(viii) Join \\(\\overline{\\mathrm{EF}}\\).<br \/>\nThen \\(\\overline{\\mathrm{EF}}\\) is the perpendicular bisector of the chord \\(\\overline{\\mathrm{AB}}\\).<br \/>\n(ix) With C as centre, using compass,<br \/>\ndraw two arcs on either side of CD.<br \/>\nThe radius of this arc should be more than half of the length of \\(\\overline{\\mathrm{CD}}\\).<br \/>\n(x) With the same radius and with D as centre,<br \/>\ndraw another two arcs using a compass.<br \/>\nLet it cut the previous circle at G and H.<br \/>\n(xi) Join \\(\\overline{\\mathrm{GH}}\\).<br \/>\nThen \\(\\overline{\\mathrm{GH}}\\) is the perpendicular bisector of the chord \\(\\overline{\\mathrm{CD}}\\).<br \/>\nWe find that perpendicular bisectots \\(\\overline{\\mathrm{EF}}\\) and \\(\\overline{\\mathrm{GH}}\\) meet at O,<br \/>\nthe centre of the circle.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80542\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-9.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.2 9\" width=\"327\" height=\"193\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-9.png 327w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.2-9-300x177.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><\/p>\n<p>Question 1.<br \/>\nDraw an angle of 80\u00b0 and make a copy of it using ruler and compass.<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(i) Construct an angle ABC = 80\u00b0.<br \/>\n(ii) Take a line l and mark a point D on it.<br \/>\n(iii) Fix the compass pointer on B and<br \/>\ndraw an arc which cuts the sides of \u2220ABC at D and E.<br \/>\n(iv) Without changing the compass setting,<br \/>\nplace the pointer on P and draw an arc which cuts l at Q.<br \/>\n(v) Open the compass equal to length DE.<br \/>\n(vi) Without disturbing the radius on compass,<br \/>\nplace its pointer at Q and draw an arc which cuts the previous arc at R.<br \/>\n(vii) Join PR and draw ray PR.<br \/>\nIts gives \u2220RPQ which is the required angle<br \/>\nwhose measure is equal to the measure of \u2220ABC.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80544\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.3-1.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.3 1\" width=\"211\" height=\"473\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.3-1.png 211w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.3-1-134x300.png 134w\" sizes=\"(max-width: 211px) 100vw, 211px\" \/><\/p>\n<p>Question 2.<br \/>\nDraw an angle of measure 127\u00b0 and construct its bisector.<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(i) Draw \\(\\overline{\\mathrm{OQ}}\\) of any length.<br \/>\n(ii) Place the centre of the protractor at O and the zero edge along \\(\\overline{\\mathrm{OQ}}\\).<br \/>\n(iii) Start with 0 near Q. Mark point P at 127\u00b0.<br \/>\n(iv) Join \\(\\overline{\\mathrm{OP}}\\). Then, \u2220POQ = 127\u00b0<br \/>\n(v) With O as centre and using compass,<br \/>\ndraw an arc that cuts both rays of \u2220POQ.<br \/>\nLabel the points of intersection as P&#8217; and Q&#8217;.<br \/>\n(vi) With Q&#8217; as centre, draw (in the interior of \u2220POQ)<br \/>\nan arc whose radius is more than half the length Q&#8217;P&#8217;.<br \/>\n(vii) With the same radius and with P&#8217; as centre,<br \/>\ndraw another arc in the interior of \u2220POQ.<br \/>\nLet the two arcs intersect at R. Then, \\(\\overline{\\mathrm{OR}}\\) is the bisector of \u2220POQ.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80545\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.3-2.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.3 2\" width=\"341\" height=\"200\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.3-2.png 341w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.3-2-300x176.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><\/p>\n<p>Question 3.<br \/>\nDraw \u2220POQ = 64\u00b0. Also draw its line of symmetry.<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(i) Draw a ray \\(\\overline{\\mathrm{OQ}}\\)<br \/>\n(ii) Place the centre of the protractor at O and the zero edge along \\(\\overline{\\mathrm{OQ}}\\).<br \/>\n(iii) Start with 0 near Q. Mark point P at 64\u00b0.<br \/>\n(iv) Join \\(\\overline{\\mathrm{OP}}\\) . Then, \u2220POQ = 64\u00b0.<br \/>\n(v) With O as centre and using compass,<br \/>\ndraw an arc that cuts both rays of \u2220POQ.<br \/>\nLabel the points of intersection as P&#8217; and Q&#8217;.<br \/>\n(vi) With Q&#8217; as centre, draw (in the interior of \u2220POQ)<br \/>\nan arc whose radius is more than half the length Q&#8217;P&#8217;.<br \/>\n(vii) With the same radius and with P&#8217; as centre,<br \/>\ndraw another arc in the interior of \u2220POQ.<br \/>\nLet the two arcs intersect at R.<br \/>\nThen, \\(\\overline{\\mathrm{OR}}\\) is the bisector of \u2220POQ<br \/>\nwhich is also the line of symmetry of \u2220POQ as \u2220POR = \u2220ROQ.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80546\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.3-3.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.3 3\" width=\"279\" height=\"264\" \/><\/p>\n<p>Question 4.<br \/>\nDraw a right angle and construct its bisector.<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(i) Draw a ray OQ.<br \/>\n(ii) Place the centre of the protractor at O and the zero edge along \\(\\overline{\\mathrm{OQ}}\\).<br \/>\n(iii) Start with 0 near Q. Mark point P at 90\u00b0.<br \/>\n(iv) Join \\(\\overline{\\mathrm{OP}}\\). Then, \u2220POQ = 90\u00b0<br \/>\n(v) With 0 as centre and using compass,<br \/>\ndraw an arc that cuts both rays of \u2220POQ.<br \/>\nLabel the points of intersection as P&#8217; and Q&#8217;.<br \/>\n(vi) With Q&#8217; as centre, draw (in the interior of \u2220POQ)<br \/>\nan arc whose radius is more than half the length Q&#8217;P&#8217;.<br \/>\n(vii) With the same radius and with P&#8217; as centre,<br \/>\ndraw another arc in the interior of \u2220POQ.<br \/>\nLet the two arcs intersect at R.<br \/>\nThen, \\(\\overline{\\mathrm{OR}}\\) is the bisector of \u2220POQ.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80547\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.3-4.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.3 4\" width=\"279\" height=\"284\" \/><\/p>\n<p>Question 5.<br \/>\nDraw an angle of 152\u00b0 and divide it into four equal parts.<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(i) Draw a ray \\(\\overline{\\mathrm{OQ}}\\).<br \/>\n(ii) Place the centre of the protractor at O and the zero edge along \\(\\overline{\\mathrm{OQ}}\\).<br \/>\n(iii) Start with 0 near Q. Mark a point P at 152\u00b0.<br \/>\n(iv) Join OP. Then, \u2220POQ =152\u00b0<br \/>\n(v) With O as centre and using compass,<br \/>\ndraw an arc that cuts both rays of \u2220POQ.<br \/>\nLabel the points of intersection as P&#8217; and Q&#8217;.<br \/>\n(vi) With Q&#8217; as centre, draw (in the interior of \u2220POQ)<br \/>\nan arc whose radius is more than half the length Q&#8217;P&#8217;.<br \/>\n(vii) With the same radius and with P&#8217; as centre,<br \/>\ndraw another arc in the interior of \u2220POQ.<br \/>\nLet the two arcs intersect at R. Then, \\(\\overline{\\mathrm{OR}}\\) is the bisector of \u2220POQ.<br \/>\n(viii)With O as centre and using compasses,<br \/>\ndraw an arc that cuts both rays of \u2220ROQ.<br \/>\nLabel the points of intersection as B and A.<br \/>\n(ix) With A as centre, draw (in the interior of \u2220ROQ)<br \/>\nan arc whose radius is more than half the length AB.<br \/>\n(x) With the same radius and with B as centre,<br \/>\ndraw another arc in the interior of \u2220ROQ.<br \/>\nLet the two arcs intersect at S. Then, \\(\\overline{\\mathrm{OS}}\\) is the bisector of \u2220ROQ.<br \/>\n(xi) With O as centre and using compass,<br \/>\ndraw an arc that cuts both rays of \u2220POR.<br \/>\nLabel the points of intersection as D and C.<br \/>\n(xii) With C as centre, draw (in the interior of \u2220POR)<br \/>\nan arc whose radius is more than half the length CD.<br \/>\n(xiii) With the same radius and with D as centre,<br \/>\ndraw another arc in the interior of \u2220POR.<br \/>\nLet the two arcs intersect at T.<br \/>\nThen, \\(\\overline{\\mathrm{OT}}\\) is the bisector of \u2220POR.<br \/>\nThus, \\(\\overline{\\mathrm{OS}}\\), \\(\\overline{\\mathrm{OR}}\\) and \\(\\overline{\\mathrm{OT}}\\) divide \u2220POQ = 152\u00b0 into four equal parts.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80549\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.3-5.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.3 5\" width=\"354\" height=\"225\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.3-5.png 354w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.3-5-300x191.png 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/p>\n<p>Question 6.<br \/>\nDraw an angle of measure 45\u00b0 and bisect it.<br \/>\nSolution:<br \/>\nSteps of construction :<br \/>\n(i) Draw a straight line BC.<br \/>\n(ii) With B as a centre and any suitable radius,<br \/>\ndraw an arc to meet BC at E.<br \/>\n(iii) With E as centre and same radius<br \/>\ndraw an arc to meet the previous arc at G.<br \/>\n(iv) With G and F as centre and same radius<br \/>\ndraw another arc to meet the first arc at H.<br \/>\n(v) With H and E as centre draw two arcs of equal radius less than \\(\\frac{1}{2}\\) GE.<br \/>\n(vi) Cutting each other at J joined BJ and produce it to D.<br \/>\n(vii) With L and E as centre draw two arcs of equal radius less than \\(\\frac{1}{2}\\) LE.<br \/>\n(viii) Cutting each other at K joined BK and produce it to I.<br \/>\n(ix) Measuring angle \u2220IBC = 22.5\u00b0<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-80550\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Ex-13.3-6.png\" alt=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.3 6\" width=\"282\" height=\"264\" \/><\/p>\n<h4><a href=\"https:\/\/www.aplustopper.com\/ml-aggarwal-icse-solutions-for-class-6-maths\/\">ML Aggarwal Class 6 Solutions for ICSE Maths<\/a><\/h4>\n","protected":false},"excerpt":{"rendered":"<p>ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Objective Type Questions Mental Maths Question 1. Fill in the blanks: (i) A ruler is used to draw line and to measure their &#8230;&#8230;&#8230;&#8230; (ii) A divider is sued to compare &#8230;&#8230;&#8230;&#8230; (iii) A compass is used to draw circles or arcs of [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[3034],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/ml-aggarwal-class-6-solutions-for-icse-maths-chapter-13-ex-13-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry\" \/>\n<meta property=\"og:description\" content=\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Objective Type Questions Mental Maths Question 1. Fill in the blanks: (i) A ruler is used to draw line and to measure their &#8230;&#8230;&#8230;&#8230; (ii) A divider is sued to compare &#8230;&#8230;&#8230;&#8230; (iii) A compass is used to draw circles or arcs of [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.aplustopper.com\/ml-aggarwal-class-6-solutions-for-icse-maths-chapter-13-ex-13-1\/\" \/>\n<meta property=\"og:site_name\" content=\"A Plus Topper\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/aplustopper\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-02-03T04:30:16+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-02-03T04:33:59+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Check-Your-Progress-1.png\" \/>\n<meta name=\"twitter:card\" content=\"summary\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasanna\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"25 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/www.aplustopper.com\/#organization\",\"name\":\"Aplus Topper\",\"url\":\"https:\/\/www.aplustopper.com\/\",\"sameAs\":[\"https:\/\/www.facebook.com\/aplustopper\/\"],\"logo\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/www.aplustopper.com\/#logo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"contentUrl\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"width\":1585,\"height\":375,\"caption\":\"Aplus Topper\"},\"image\":{\"@id\":\"https:\/\/www.aplustopper.com\/#logo\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.aplustopper.com\/#website\",\"url\":\"https:\/\/www.aplustopper.com\/\",\"name\":\"A Plus Topper\",\"description\":\"Improve your Grades\",\"publisher\":{\"@id\":\"https:\/\/www.aplustopper.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.aplustopper.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/www.aplustopper.com\/ml-aggarwal-class-6-solutions-for-icse-maths-chapter-13-ex-13-1\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Check-Your-Progress-1.png\",\"contentUrl\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-6-Solutions-for-ICSE-Maths-Chapter-13-Practical-Geometry-Check-Your-Progress-1.png\",\"width\":233,\"height\":196,\"caption\":\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Check Your Progress 1\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.aplustopper.com\/ml-aggarwal-class-6-solutions-for-icse-maths-chapter-13-ex-13-1\/#webpage\",\"url\":\"https:\/\/www.aplustopper.com\/ml-aggarwal-class-6-solutions-for-icse-maths-chapter-13-ex-13-1\/\",\"name\":\"ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry - 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