Question

in ABC, AC=BC and angle ACB=90° then prove AB2=2AC?​

Answer 1

$\bold{Answer:}}$

In,  ΔABC  AC=BC ,

So, perpendicular = base.

ACB=90°(this tells that it is a right-angled triangle),

To prove  AB²=2AC²,

Here,

Hypotenuse=AB,

Also we know thatΔABC is a isosceles triangle.

Hence AC=BC(Isosceles triangle has 2 sides equal),

Using pythagoras theorem in ΔACB

(Hypotenuse²)=(perpendicular)²+(base)²,

AB²=AC²+BC²,

AB²=AC²+AC²,

AB²=2AC²(proved).