Question

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

Answer 1

Answer:

Step-by-step explanation:

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

${AB}^{2} = 2 {AC}^{2} \\ {AB}^{2} \: = {AC}^{2} + \: {AB}^{2}$
By applying converse of Pythagoras theorem,

We get that AB is hypotenuse,

C = 90 degree

Thus ABC is an right angle Triangle