(Q15) ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2.

Solution :

ABC

Given : In ∆ABC; ∠C = 90° AC = BC.

R.T.P : AB2 = 2AC2

Proof : In ∆ACB; ∠C = 90°

Hence, AC2 + ( )2 = ( )2

[Square of the hypotenuse is equal to sum of the squares of the other two sides - Pythagoras theorem]

⇒ AC2 + ( )2 = ( )2 [∵ AC = BC given]

⇒ AB2 = 2( )2