With of the following triangle congruence shortcuts could be used to prove PRQ = TRS Given Data, ∠Q=∼∠S QR―=∼SR― a)Side-Side-Side Postulate (SSS) b)Side-Angle-Side Postulate (SAS) c)Angle-Side-Angle Postulate (ASA) d)Angle-Angle-Side Theorem (AAS)

"With of the following triangle congruence shortcuts could..." was answered by our community

BenoguigoliB

Answered question

2020-12-06

With of the following triangle congruence shortcuts could be used to prove PRQ = TRS

Given Data,
$∠ Q \tilde{=} ∠ S$
$\overset{―}{Q R} \tilde{=} \overset{―}{S R}$
a)Side-Side-Side Postulate (SSS)
b)Side-Angle-Side Postulate (SAS)
c)Angle-Side-Angle Postulate (ASA)
d)Angle-Angle-Side Theorem (AAS)

Answer & Explanation

Ezra Herbert

Skilled2020-12-07Added 99 answers

Step 1
It is given that,

∠ Q \tilde{=} ∠ S

\overset{―}{Q R} \tilde{=} \overset{―}{S R}

I n △ P Q R and △ R S T

∠ Q \tilde{=} ∠ S

(equal angles given)

\overset{―}{Q R} \tilde{=} \overset{―}{S R}

( equal sides given)

∠ P R Q \tilde{=} ∠ S R T

( vertically opposite angles)
Here, two angles and one side of both triangle is equal then,
Step 2

△ P Q R \tilde{=} △ R S T

(By angle-side-angle congruence)
Hence option C is correct.

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