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Properties of Angles Formed by Two Parallel Lines and a Transversal

In triangle P...

Question

In triangle PQR, PQ = PR and PM is perpendicular to QR. By which property is triangle PQM congruent to triangle PRM?

RHS

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SSS

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SAS

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AAS

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Solution

The correct option is A RHS

Consider $△ P Q M and △ P R M$
PQ = PR (given)
PM = PM (common side)
$∠ P M Q = ∠ P M R = 90^{o}$ $(Since P M ⊥ Q R)$

Hence the two triangles are congruent by RHS congruence criterion.

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