# ABC is an isosceles triangle with AC = BC. If AB^{2} = 2AC^{2}, prove that ABC is a right triangle

**Solution:**

As we know, in a triangle, if the square of one side is equal to the sum of the square of the other two sides then the angle opposite the first side is a right angle.

In ΔABC

It is given that AC = BC and AB^{2} = 2 AC^{2}

⇒ AB^{2} = AC^{2} + AC^{2}

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

As the above equation satisfies Pythagoras theorem, we can say that

⇒ ∠ACB = 90°

⇒ Therefore, ΔABC is a right triangle

**Video Solution:**

## ABC is an isosceles triangle with AC = BC. If AB^{2} = 2AC^{2}, prove that ABC is a right triangle

### NCERT Class 10 Maths Solutions - Chapter 6 Exercise 6.5 Question 5:

ABC is an isosceles triangle with AC = BC. If AB^{2} = 2AC^{2}, prove that ABC is a right triangle

In the above figure, ABC is an isosceles triangle with AC = BC. If AB^{2} = 2AC^{2}, hence it is proved that ABC is a right triangle