**Triangles**

**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:**

We have ∆ABC ~ ∆DEF

**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.

**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:

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

**Solution:**

**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:**

**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:**

**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:**

**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:**