**CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.5 Question 7**

**7.** Prove that the sum of squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

**Solution:**

**Given: **ABCD is a rhombus. Diagonals AC and BD of rhombus intersect at point O.

**To Prove: **

**Proof:**

In

{Diagonals of rhombus intersect at 90}

Therefore, {By, pythagoras theorem} ** (1)**

Similarly, {By, pythagoras theorem} ** (2)**

Similarly, {By, pythagoras theorem} ** (3)**

Similarly, {By, pythagoras theorem} ** (4)**

Adding **(1)**, **(2)**, **(3)** and **(4)**, we get

**(5)**

But, we have OA = OC and OB = OD **{Diagonals of rhombus bisect each other} (6)**

Putting **(6) in (5), **we get

**{2OA = AC and 2OB= BD}**

**Hence Proved**