If $△ P Q R$ is an isosceles right triangle, right-angled at $R$ . Prove that ${P Q}^{2} = 2 {P R}^{2}$

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Solution

As $Δ P Q R$ is right angled at R, then,

$P Q^{2} = Q R^{2} + P R^{2}$

Since the triangle is an isosceles triangle, then, $Q R = P R$ , therefore,

$P Q^{2} = P R^{2} + P R^{2}$

$P Q^{2} = 2 P R^{2}$

Hence proved.

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