**CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.4 Question 6**

**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:**

**Given: ** ~ . AP is the median to side BC of and DQ is the median to side EF of .

{Corresponding sides of similar triangles are proportional}

**(1)**

**{P is the mid-point of BC and Q is the mid-point of EF}**

**To Prove: **

**Proof:**

**{The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides}**

** (2)**

In and

from **(1)**

And, ** {Corresponding angles of similar triangles are equal}**

Therefore, by **SAS similarity criterion**, ~

Therefore, **(3)**

Putting **(3)** in **(2)**, we get

**Hence Proved**