**CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.5 Question 5**

**5.** ABC is an isosceles triangle with AC = BC. If, , prove that ABC is a right triangle.

**Solution:**

**Given: **ABC is an isosceles triangle with **.**

**To Prove: ** is a right angled triangle.

**Proof: **It is given that ABC is an isosceles triangle with . It means AB is the biggest side of triangle. Hence, we have BC = AC. **(1)**

**.**

**(2)**

Putting **(1)** in **(2), **we get

Therefore, by converse of pythagoras theorem, is right angled at C.

**{In a triangle, if square of one side is equal to sum of squares of other two sides then the given triangle is right angled}**

**Hence Proved**