Question

ABC is an isosceles triangle with AC = BC. If AB² = 2AC², Prove that ABC is a right triangle.​

Answer 1

Answer:

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

ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.

In ΔABC,

It is given that AC = BC and AB2 = 2 AC2

⇒ AB2 = AC2 + AC2

⇒ AB2 = AC2 + BC2 [Since AC = BC]

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

⇒ ∠ACB = 90°

Therefore, ΔABC is a right triangle