$A B C$ is an isosceles triangle and $∠ B = 90^{o}$ , then show that ${A C}^{2} = 2 {A B}^{2}$ .

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Solution

$A B C$ is a right angle triangle.
Given that $A C^{2} = 2 A B^{2}$
$A C^{2} = A B^{2} + A B^{2}$ .....(Since it is isosceles $A B = B C$ )
$A C^{2} = A B^{2} + B C^{2}$
The traingle is satisfying the pythagoras theorem.
Therefore, the given triangle is right-angle triangle.

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