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Answer :
By the AAS congruence theorem, [tex](\triangle PQR \cong \triangle TSR)[/tex].
The given information is that [tex](QR \cong SR)[/tex], and[tex](\angle PQR \cong \angle TSR)[/tex]. We need to prove that [tex](\triangle PQR \cong \triangle TSR)[/tex].
To prove that [tex](\triangle PQR \cong \triangle TSR)[/tex], we can use the AAS congruence theorem. According to the AAS congruence postulate (we have two pairs of congruent angles and the included side congruent) Therefore, we have proven that ΔPQR ≅ ΔTSR.
Statement: Reason
[tex](QR \cong SR)[/tex] (Given)
[tex](\angle PQR \cong \angle TSR)[/tex] (Given)
∠PRT ≅ ∠ QRS Vertical Angles Property
[tex](QR \cong SR)[/tex] (Given)
[tex](\triangle PQR \cong \triangle TSR)[/tex] AAS Congruence Property.
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