Question

Given that SQ⎯⎯⎯⎯⎯ bisects ∠PSR and PS⎯⎯⎯⎯⎯≅SR⎯⎯⎯⎯⎯, which of the following triangle congruence statements can be used to prove that ∠P≅∠R?

The figure shows two triangles P S Q and R S Q with a common side S Q.

Answer 1

The congruency proof that can be used to show that ∠P≅∠R is as given in the steps below.

How to prove Triangle Congruence?

From the figure as seen online, we can see that;

The figure shows the same triangles PQS and RQS as in the beginning of the task. Angles SPQ and SRQ are highlighted in red.

Thus, the 2 column proof to show that ∠P≅∠R is;

Statement 1; ∠SPQ≅∠SRQ

Reason 1; Given

Statement 2; SQ bisects ∠PSR

Reason 2; Given

Statement 3; ∠PSQ≅∠QSR

Reason 3; Definition of angle bisector

Statement 4; SQ ≅ SQ

Reason 4; Reflexive Property of Congruence

Statement 5; △PQS≅△RQS

Reason 5; Angle - Angle Side (AAS) Congruency Postulate

Statement 6; PS ≅ SR

Reason 6; CPCTC (Corresponding parts of congruent triangles are congruent)

Read more about Triangle Congruence at; https://brainly.com/question/7727792

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