Life begins at the end of your comfort zone. – **Neale Donald Walsh**

# Lecture - 8 Chapter 6 Triangles

**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