# ABC is an isosceles triangle right angled at C. Prove that AB^{2} = 2AC^{2}

**Solution:**

As we are aware, in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

In ΔABC, ∠ACB = 90° and AC = BC

Using Pythagoras theorem,

⇒ AB^{2} = AC^{2} + BC^{2}

⇒ AB^{2} = AC^{2}+ AC^{2 } [Since AC = BC]

Therefore, AB^{2} = 2 AC^{2}

**Video Solution:**

## ABC is an isosceles triangle right angled at C. Prove that AB^{2} = 2AC^{2}

### NCERT Class 10 Maths Solutions - Chapter 6 Exercise 6.5 Question 4:

ABC is an isosceles triangle right angled at C. Prove that AB^{2} = 2AC^{2}

In the above figure ABC is an isosceles triangle right angled at C. Hence it is proved that AB^{2} = 2AC^{2}