**NCERT Exercise 6.4 (Part 1)**

**Proof of Theorem 6.6 :** The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

**Question 1.** Let ∆ ABC ~ ∆ DEF and their areas be, respectively, 64 cm^{2} and 121 cm^{2} . If EF = 15.4 cm, find BC.

**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.

**Question 3.** In Fig. 6.44, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that \frac{ar (ABC)}{ar (DBC)} = \frac{AO}{DO}

**Question 4.** If the areas of two similar triangles are equal, prove that they are congruent.

**NCERT Exercise 6.4 (Part 2)**

**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.

**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.

**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.

**Question 8.** 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

**Question 9.** Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio