**Ex 6.4 Class 10 Maths Question 1.**

Let ∆ABC ~ ∆DEF and their areas be, respectively, 64 cm^{2} and 121 cm^{2}. If EF = 15.4 cm, find BC.

**Solution for Ex 6.4 Class 10 Maths Question 1**

**Solution for Ex 6.4 Class 10 Maths Question 1**

**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 for Ex 6.4 Class 10 Maths Question 2**

**Solution for Ex 6.4 Class 10 Maths Question 2**

**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:

**Solution for Ex 6.4 Class 10 Maths Question 3**

**Solution for Ex 6.4 Class 10 Maths Question 3**

**Ex 6.4 Class 10 Maths Question 4.**

If the areas of two similar triangles are equal, prove that they are congruent.

**Solution for Ex 6.4 Class 10 Maths Question 4**

**Solution for Ex 6.4 Class 10 Maths Question 4**

**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 for Ex 6.4 Class 10 Maths Question 5**

**Solution for Ex 6.4 Class 10 Maths Question 5**

**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 for Ex 6.4 Class 10 Maths Question 6**

**Solution for Ex 6.4 Class 10 Maths Question 6**

**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 for Ex 6.4 Class 10 Maths Question 7**

**Solution for Ex 6.4 Class 10 Maths Question 7**

**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

**Solution for Ex 6.4 Class 10 Maths Question 8 (i)**

**Solution for Ex 6.4 Class 10 Maths Question 8 (i)**

**(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 for Ex 6.4 Class 10 Maths Question 8 (ii)**

**Solution for Ex 6.4 Class 10 Maths Question 8 (ii)**