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Triangle Inequality

In a triangle...

Question

In a triangle PQR, X and Y are 2 points on PQ and QR respectively If PQ=QR and QX=QY show that PX=RY.

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Solution

$P Q = Q R$
$⟹ P X + X Q = Q Y + Y R$
$⟹ P X = Y R + (Q Y - X Q)$
$(∵ Q Y = Q X, P X = Y R + 0)$
$⟹ P X = Y R$

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