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

AcademicMathematicsNCERTClass 10

Given:

ABC is an isosceles triangle with AC = BC and $AB^2 = 2AC^2$.

To do: 

We have to prove that ABC is a right triangle.

Solution:


In $∆ABC$, 

$AB^2 = 2AC^2$.

$AB^2= AC^2 + AC^2$

$AB^2 = AC^2 + BC^2$

This implies, by converse of Pythagoras theorem,

$\angle ACB= 90^o$

Therefore,

ABC is a right triangle.

Hence proved.

raja
Updated on 10-Oct-2022 13:21:26

Advertisements