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AAS Criteria for Congruency

In Figure, PS...

Question

In Figure, PS = QR and $∠ S P Q = ∠ R Q P$ .

Prove that PR = QS and $∠ Q P R = ∠ P Q S$ .

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Solution

In $Δ S P Q a n d Δ R Q P,$ we have
PS = QR [Given]
$∠ S P Q = ∠ R Q P$ [Given]
PQ = PQ [Common]
Therefore, by SAS criterion of congruence, we have
$Δ S P Q ≅ Δ R Q P$
$\Rightarrow S Q = R P a n d ∠ Q P R = ∠ P Q S$ (c.p.c.t.)

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