We are asked to write a paragraph proof to prove that triangles QRT and SRT are congruent. Here is what we are given.
Given:& QR ≅ SR, ST ≅ QT
Two pairs of sides in the triangles are congruent. Let's then mark the congruent sides in the given diagram.
Notice that the side RT is common for both △ QRT and △ SRT. By the Reflexive Property of Congruent Segments we have RT is congruent to itself. Let's write down what we know so far.
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QR ≅ SR & Side
QT ≅ ST & Side
RT ≅ RT & Side
All corresponding sides in the triangles are congruent. By the Side-Side-Side (SSS) Congruence Postulate, we can conclude that triangles QRT and SRT are congruent.
△ QRT ≅ △ SRT
Paragraph Proof
Let's now summarize our findings in one paragraph.
Given:& QR ≅ SR, ST ≅ QT
Prove:& △ QRT ≅ △ SRT
Proof: The side RT is common for both △ QRT and △ SRT, and by the Reflexive Property of Congruent Segments we have RT ≅ RT. Therefore, the three sides of △ QRT are congruent to the three sides of △ SRT. By the Side-Side-Side (SSS) Congruence Postulate we conclude that △ QRT ≅ △ SRT.
