Question

ABC is an isosceles triangle with AC=BC.if AB²=2AC²,Prove that ABC is a right triangle​

Answer 1

Answer:

Step-by-step explanation:

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 ]

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Answer 2

Given, ∆ABC is an isosceles triangle

Therefore AC=BC....(1)

Also given that,

(AB)²=2(AC)²

therefore (AB)²=(AC)²+(AC)²....(2)

therefore from (1) and (2),

(AB)²=(AC)²+(BC)²

Hence by Converse of Pythagoras theorem,

∆AB is an isosceles right-angled triangle. [Hence proved]