Question

ABC is an isosceles triangle with AC= BC. If AB^2 = 2AC^2 prove that it is a right angled 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 ]

Hence, triangle ABC is a right-angled triangle at C .

$\huge{\boxed{\boxed{HENCE\:\:PROVED}}}$

Answer 2

Answer

__________

Answer:

Given: AC = BC

ABC is an isoceles triangle

AB2 = 2 AC2

To prove: ABC is a right triangle

Proof: For ABC to be a right triangle, it should satify pythagoras theorem

i.e AB2 = AC2 + BC2

Now, AC = BC (given)

On substitution, we find

AB2 = 2 AC2, which is true according to the question.

So, the given sides form pythorian triplets.

Hence ABC to be a right triangle right angled at C.

Thanks ☺☺