# Ex.6.5 Q5 Triangles Solution - NCERT Maths Class 10

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## Question

$$ABC$$ is an isosceles triangle with $${AC = BC}$$. If , $$A B^{2}=2 A C^{2}$$ prove that $$ABC$$ is a right triangle.

Diagram

## Text Solution

Reasoning:

As we know ,In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Steps:

In $$\Delta A B C$$

$\rm{A C} =\rm{B C}$

\begin{align} {\rm{And}} \,A B^{2} &=2 A C^{2} \\ &=A C^{2}+A C^{2} \\ A B^{2} &=A C^{2}+B C^{2}[\because A C=B C] \end{align}

$$\Rightarrow \angle A C B=90^\circ$$

\begin{align}\Rightarrow \Delta A B C \end{align}  is a right triangle

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