Question

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

Answer 1

So, since C is your right angle, the opposite line, which is AB, is the hypotenuse.

So, by the pythagorean relation,

AB^2 = AC^2+ BC^2.

and it is also given that the triangle is isosceles. this means that 2 of the sides are equal in length. But since the hypotenuse is the longest side, it can't be equal to any other side, which means that AC = BC.

Therefore, AC^2 = AB^2.

so substituting AC^2 for BC^2 we get,

AB^2 = AC^2 + Ac^2

which implies that

AB^2= 2AC^2

Hope my answer helped ya!!! And, if it did, pleeeeeeease make sure to mark me brainliest... :)

Answer 2

By Pythagoras theorem ,
AB^2=AC^2+BC^2
Since it is an isosceles triangle AC=BC
AB^2=AC^2+AC^2
AB^2=2AC^2