Lecture-8

00:00:30 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.

00:13:30 NCERT Exercise 6.4 Question 1 Let ∆ ABC ~ ∆ DEF and their areas be, respectively, 64 cm^2 and 121 cm2 . If EF = 15.4 cm, find BC.

00:17:00 NCERT Exercise 6.4 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.

00:22:50 NCERT Exercise 6.4 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 ar (ABC)/ar (DBC)=AO/DO

00:29:10 NCERT Exercise 6.4 Question 4 If the areas of two similar triangles are equal, prove that they are congruent.

00:34:50 NCERT Exercise 6.4 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.

00:44:30 NCERT Exercise 6.4 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.

00:52:50 NCERT Exercise 6.4 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.

01:01:10 NCERT Exercise 6.4 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

01:04:20 NCERT Exercise 6.4 Question 9 Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio