Question

Triangle ABC is an isosceles triangle ,right angle at C.prove that AB square=2ACsquare

Answer 1

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Answer 2

SOLUTION :

Given :

ΔABC is a right triangle,

Also, ΔABC is isosceles triangle.

To prove:

AB² = 2AC²

Proof:

Here,

Hypotenuse = AB

Also, as it is given that, ΔABC is isosceles,

AC = BC   [equal sides of isosceles Δ]

Using Pythagoras theorem,

In Δ ABC, we have ;

AB² = AC² + BC²

AB² = AC² + AC² [AC = BC]

AB² = 2 AC²

             Hence proved.

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Extra information ;

In isosceles triangle, two sides are equal.

According to Pythagoras theorem, (Hypotenuse)² = (Base)² + (Altitude)²