• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer
  • ICSE Solutions
    • ICSE Solutions for Class 10
    • ICSE Solutions for Class 9
    • ICSE Solutions for Class 8
    • ICSE Solutions for Class 7
    • ICSE Solutions for Class 6
  • Selina Solutions
  • ML Aggarwal Solutions
  • ISC & ICSE Papers
    • ICSE Previous Year Question Papers Class 10
    • ISC Previous Year Question Papers
    • ICSE Specimen Paper 2021-2022 Class 10 Solved
    • ICSE Specimen Papers 2020 for Class 9
    • ISC Specimen Papers 2020 for Class 12
    • ISC Specimen Papers 2020 for Class 11
    • ICSE Time Table 2020 Class 10
    • ISC Time Table 2020 Class 12
  • Maths
    • Merit Batch

A Plus Topper

Improve your Grades

  • CBSE Sample Papers
  • HSSLive
    • HSSLive Plus Two
    • HSSLive Plus One
    • Kerala SSLC
  • Exams
  • NCERT Solutions for Class 10 Maths
  • NIOS
  • Chemistry
  • Physics
  • ICSE Books

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test

October 8, 2018 by Nirmala

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test

These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test.

ML Aggarwal SolutionsICSE SolutionsSelina ICSE Solutions

Question 1.
In the given figure, ∠1 = ∠2 and ∠3 = ∠4. Show that PT x QR = PR x ST.
Solution:
Given : In the given figure,
∠1 = ∠1 and ∠3 = ∠4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q1.1
To prove : PT x QR = PR x ST
Proof: ∠1 = ∠2
Adding ∠6 to both sides
∠1 + ∠6 = ∠2 + ∠6
∠SPT = ∠QPR
In ∆PQR and ∆PST
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q1.2

Question 2.
In the adjoining figure, AB = AC. If PM ⊥ AB and PN ⊥ AC, show that PM x PC = PN x PB.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q2.1
Solution:
Given : In the given figure,
AB = AC, PM ⊥ AB and PN ⊥ AC
To prove : PM x PC = PN x PB
Proof: In ∆ABC, AB = AC
∠B = ∠C
Now in ∆CPN and ∆BPM,
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q2.2

Question 3.
(a) In the figure (1) given below. ∠AED = ∠ABC. Find the values of x and y.
(b) In the fig. (2) given below, CD = \(\\ \frac { 1 }{ 2 } \) AC, B is mid-point of AC and E is mid-point of DF. If BF || AG, prove that :
(i) CE || AG
(ii) 3 ED = GD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q3.1
Solution:
(a) Given : In following figure, ∠AED = ∠ABC
Required : The values of x and y.
Now, in ∆ABC and ∆ADE
∠AED = ∠ABC (given)
∠A = ∠A (common)
∴ ∆ABC ~ ∆ADE
(By A.A. axiom of similarity)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q3.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q3.3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q3.4

Question 4.
In the given figure, 2 AD = BD, E is mid-point of BD and F is mid-point of AC and EC || BH. Prove that:
(i) DF || BH
(ii) AH = 3 AF.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q4.1
Solution:
Given : E is the mid-point of BD and F is mid-point of AC also 2 AD = BD and EC || BH
To Prove : (i) DF || BH
(ii) AH = 3 AF
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q4.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q4.3

Question 5.
In a ∆ABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm, find BD and CE.
Solution:
Given : In ∆ABC, D and E are the points on the sides AB and AC respectively
DE || BC
AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm, BC = 5 cm
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q5.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q5.2

Question 6.
In a ∆ABC, D and E are points on the sides AB and AC respectively such that AD = 5.7cm, BD = 9.5cm, AE = 3.3cm and AC = 8.8cm. Is DE || BC? Justify your answer.
Solution:
In ∆ABC, D and E are points on the sides AB and AC respectively
AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and AC = 8.8 cm
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q6.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q6.2

Question 7.
In a ∆ABC, DE is parallel to the base BC, with D on AB and E on AC. If \(\frac { AD }{ DB } =\frac { 2 }{ 3 } ,\frac { BC }{ DE } \)
Solution:
In ∆ABC, DE || BC
D is on AB and E is on AC
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q7.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q7.2

Question 8.
If the area of two similar triangles are 360 cm² and 250 cm² and if one side of the first triangle is 8 cm, find the length of the corresponding side of the second triangle.
Solution:
Let ∆ABC and ∆DEF are similar and area of
∆ABC = 360 cm²
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q8.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q8.2

Question 9.
In the adjoining figure, D is a point on BC such that ∠ABD = ∠CAD. If AB = 5 cm, AC = 3 cm and AD = 4 cm, find
(i) BC
(ii) DC
(iii) area of ∆ACD : area of ∆BCA.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q9.1
Solution:
In ∆ABC and ∆ACD
∠C = ∠C (Common)
∠ABC = ∠CAD (given)
∴ ∆ABC ~ ∆ACD
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q9.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q9.3

Question 10.
In the adjoining figure the diagonals of a parallelogram intersect at O. OE is drawn parallel to CB to meet AB at E, find area of DAOE : area of ||gm ABCD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q10.1
Solution:
(a) In the figure
Diagonals of parallelogram ABCD are AC and BD which intersect each other at O.
OE is drawn parallel to CB to meet AB in E.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q10.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q10.3

Question 11.
In the given figure, ABCD is a trapezium in which AB || DC. If 2AB = 3DC, find the ratio of the areas of ∆AOB and ∆COD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q11.1
Solution:
In the given figure, ABCD is trapezium in
which AB || DC, 2AB = 3DC
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q11.2

Question 12.
In the adjoining figure, ABCD is a parallelogram. E is mid-point of BC. DE meets the diagonal AC at O and meet AB (produced) at F. Prove that .
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q12.1
(i) DO : OE = 2 : 1
(ii) area of ∆OEC : area of ∆OAD = 1 : 4.
Solution:
Given : In || gm ABCD,
E is mid point of BC and DE meets the diagonal AC at O and meet AB produced at F.
To prove : (i) DO : OE = 2 : 1
(ii) area of ∆OEC : area of ∆OAD = 1 : 4
Proof: In ∆AOD and ∆EDC
∠AOD = ∠EOC (vertically opposite angle)
∠OAD = ∠OCB (alt. angles)
∆AOD ~ ∆EOC (AA postulate)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q12.2

Question 13.
A model of a ship is made to a scale of 1 : 250. Calculate :
(i) the length of the ship, if the length of model is 1.6 m.
(ii) the area of the deck of the ship, if the area of the deck of model is 2.4 m².
(iii) the volume of the model, if the volume of the ship is 1 km³.
Solution:
Scale factor (k) of the model of the ship = \(\\ \frac { 1 }{ 250 } \)
(i) Length of model = 1.6 m
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test Q13.1

Hope given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 14 Similarity Chapter Test are helpful to complete your math homework.

If you have any doubts, please comment below. APlusTopper try to provide online math tutoring for you.

Filed Under: ML Aggarwal ICSE

Primary Sidebar

  • MCQ Questions
  • RS Aggarwal Solutions
  • RS Aggarwal Solutions Class 10
  • RS Aggarwal Solutions Class 9
  • RS Aggarwal Solutions Class 8
  • RS Aggarwal Solutions Class 7
  • RS Aggarwal Solutions Class 6
  • ICSE Solutions
  • Selina ICSE Solutions
  • Concise Mathematics Class 10 ICSE Solutions
  • Concise Physics Class 10 ICSE Solutions
  • Concise Chemistry Class 10 ICSE Solutions
  • Concise Biology Class 10 ICSE Solutions
  • Concise Mathematics Class 9 ICSE Solutions
  • Concise Physics Class 9 ICSE Solutions
  • Concise Chemistry Class 9 ICSE Solutions
  • Concise Biology Class 9 ICSE Solutions
  • ML Aggarwal Solutions
  • ML Aggarwal Class 10 Solutions
  • ML Aggarwal Class 9 Solutions
  • ML Aggarwal Class 8 Solutions
  • ML Aggarwal Class 7 Solutions
  • ML Aggarwal Class 6 Solutions
  • HSSLive Plus One
  • HSSLive Plus Two
  • Kerala SSLC

Recent Posts

  • Advantages and Disadvantages of Online Shopping | Pros and Cons, Benefits of Online Shopping
  • वर्ण विभाग – हिन्दी वर्ण, वर्णमाला, परिभाषा, भेद और उदाहरण
  • Roopak Alankar – रूपक अलंकार, परिभाषा उदाहरण अर्थ हिन्दी एवं संस्कृत
  • Essay on Forest | Long and Short Essay on Forest in English for Children and Students
  • Advantages And Disadvantages Of Entrepreneurship | What is Entrepreneurship?, Pros and Cons, Benefits and Drawbacks
  • Focussed vs Focused | Which is Correct? Difference Between Focussed and Focused
  • Advantages and Disadvantages of Hydropower Plant | What are Hydropower Plants?
  • Physics Symbols and Their Names
  • How to Address a Letter | Format and Sample of Addressing a Letter
  • EWS Certificate | Application Process, Documents Required, Format, How To Apply?
  • 11 Sample Follow Up Letters | Format, Examples and How To Write Follow-up Letters?

Footer

  • RS Aggarwal Solutions
  • RS Aggarwal Solutions Class 10
  • RS Aggarwal Solutions Class 9
  • RS Aggarwal Solutions Class 8
  • RS Aggarwal Solutions Class 7
  • RS Aggarwal Solutions Class 6
  • Picture Dictionary
  • English Speech
  • ICSE Solutions
  • Selina ICSE Solutions
  • ML Aggarwal Solutions
  • HSSLive Plus One
  • HSSLive Plus Two
  • Kerala SSLC
  • Distance Education
DisclaimerPrivacy Policy
Area Volume Calculator