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NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4.

  • Triangles Class 10 Ex 6.1
  • Triangles Class 10 Ex 6.2
  • Triangles Class 10 Ex 6.3
  • Triangles Class 10 Ex 6.4
  • Triangles Class 10 Ex 6.5
  • Triangles Class 10 Ex 6.6
Board CBSE
Textbook NCERT
Class Class 10
Subject Maths
Chapter Chapter 6
Chapter Name Triangles
Exercise Ex 6.4
Number of Questions Solved 8
Category NCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4

Ex 6.4 Class 10 Maths Question 1.
Let ∆ABC ~ ∆DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.
Solution:
We have ∆ABC ~ ∆DEF
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 55

Ex 6.4 Class 10 Maths Question 2.
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.
Solution:
In the figure below, a trapezium ABCD is shown, in which AB || DC  and AB = 2DC. Its diagonals interest each other at the point O.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 56

Ex 6.4 Class 10 Maths Question 3.
In the given figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that: \(\frac { ar\left( ABC \right) }{ ar\left( DBC \right) } =\frac { AO }{ DO } \)
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 57
Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 58

Ex 6.4 Class 10 Maths Question 4.
If the areas of two similar triangles are equal, prove that they are congruent.
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 59

Ex 6.4 Class 10 Maths Question 5.
D, E and F are respectively the mid-points of sides AB, BC and CA of ∆ABC. Find the ratio of the areas of ∆DEF and ∆ABC.
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 60

Ex 6.4 Class 10 Maths Question 6.
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 61
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 62

Ex 6.4 Class 10 Maths Question 7.
Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 63

Ex 6.4 Class 10 Maths Question 8.
Tick the correct answer and justify
(i) ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is

(a) 2:1
(b) 1:2
(c) 4:1
(d) 1:4
(ii) Sides of two similar triangles are in the ratio 4:9. Areas of these triangles are in the ratio
(a) 2 :3
(b) 4:9
(c) 81:16
(d) 16:81
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 64
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 65

 

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 6.4, drop a comment below and we will get back to you at the earliest.

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