Question

ABC is an isosceles triangle with AC=BC.if AB^=2AC^,Prove that ABC is a right triangle

Answer 1

Hello !

Δ ABC is an isosceles triangle  with AC = BC , and AB² = 2AC²

To prove : ∠C = 90°

Proof :-

AB² = 2AC²
       = AC² + AC²
       = AC² + BC²                                  [ ∵ AC = BC ]
AB² = AC² + BC²     ----> (1)

From (1) , 
∠C = 90° [ by converse of Pythagoras theorem ]

Answer 2

hey

in the question it is given that

AC=BC ------------------(1)

AND AB^ =AB^+2AC^-------------(2)

by substituinv eq 1 in eq 2 we get

AB^=AC^+AC^

THEREFORE.

angle C=90°

(BY CONVSE OF PYTHAGORAS THEOREM )

HOPE THIS HELPS YOU