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NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.2

December 26, 2018 by Dattu

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.2 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 6 Triangles Class 10 NCERT Solutions Ex 6.2. 

  • Triangles Class 10 Ex 6.1
  • Triangles Class 10 Ex 6.3
  • Triangles Class 10 Ex 6.4
  • Triangles Class 10 Ex 6.5
  • Triangles Class 10 Ex 6.6
BoardCBSE
TextbookNCERT
ClassClass 10
SubjectMaths
ChapterChapter 6
Chapter NameTriangles
ExerciseEx 6.2
Number of Questions Solved10
CategoryNCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.2

NCERT Solutions for Class 10 Maths

Page No: 128

Question 1. (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 6

Solution:
(i)
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 7
Let EC = x
Since DE || BC.
Therefore, by basic proportionality theorem,
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 8

(ii)
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 9
Let AD = x
Since DE || BC,
Therefore by basic proportionality theorem,
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 10

Question 2. E and F are points on the sides PQ and PR respectively of a ΔPQR.
For each of the following cases, state whether EF || QR.
(i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm
(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.63 cm

Solution:
(i)
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 11
Given that PE = 3.9, EQ = 3, PF = 3.6, FR = 2.4
Now,
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 12
(ii)
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 13
PE = 4, QE = 4.5, PF = 8, RF = 9
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 14
(iii)
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 15
PQ = 1.28, PR = 2.56, PE = 0.18, PF = 0.36
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 16

Question 3. In the fig 6.18, if LM || CB and LN || CD, prove that
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 17

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 18
In the given figure
Since LM || CB,
Therefore by basic proportionality theorem,
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 19

Question 4. In figure , DE || AC and DF || AE. Prove that 
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 20

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 21
In ∆ABC,
Since DE || AC
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 22
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 23

Question 5. In figure , DE || OQ and DF || OR, show that EF || QR.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 24

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 25
In ∆POQ
Since DE || OQ
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 26
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 27
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 28

Question 6. In the figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 29

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 30

Question 7. Using Basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 31
Consider the given figure
PQ is a line segment drawn through midpoint P of line AB such that PQ||BC
i.e. AP = PB
Now, by basic proportionality theorem
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 32
i.e. AQ = QC
Or, Q is midpoint of AC.

Question 8. Using Converse of basic proportionality theorem, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 33
Consider the given figure
PQ is a line segment joining midpoints P and Q of line AB and AC respectively.
i.e. AP = PB and AQ = QC
Now, we may observe that
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 34
And hence basic proportionality theorem is verified
So, PQ||BC

Question 9. ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O.
Show that \(\frac { AO }{ BO } =\frac { CO }{ DO } \)

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 35

Question 10. The diagonals of a quadrilateral ABCD intersect each other at the point O such that \(\frac { AO }{ BO } =\frac { CO }{ DO } \). Show that ABCD is a trapezium.

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 36

 

We hope the NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.2 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.2, drop a comment below and we will get back to you at the earliest.

Filed Under: CBSE Tagged With: NCERT Solutions for Class 10 Maths

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