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Given: ∠P ≅ ∠Q and Line Segment RS bisects ∠PQR. Prove: Line segments PR≅QR . Supply the missing statement in Statement 5 of the proof of the the Converse of the Isosceles Triangle Theorem.

Begin with isosceles ∆PRQ with ∠P ≅ ∠Q. Construct Line Segment RS a bisector of ∠PRQ.

A. ∆PRS ≅ ∆PRQ


B. ∆PRS ≅ ∆PRS


C. ∆PRS ≅ ∆SRQ


D. ∆PRS ≅ ∆QRS

Given P Q and Line Segment RS bisects PQR Prove Line segments PRQR Supply the missing statement in Statement 5 of the proof of the the Converse of the Isosceles class=
Given P Q and Line Segment RS bisects PQR Prove Line segments PRQR Supply the missing statement in Statement 5 of the proof of the the Converse of the Isosceles class=

Respuesta :

Medunno13

Answer:

D

Step-by-step explanation:

Vertices P and Q correspond, vertices R and S correspond to themselves.

ashishdwivedilVT

By the property of (Angle-Angle-Side)AAS postulates ΔPRS≅QRS

Option (D) is correct.

It is required to find the missing statement in Statement 5 of the proof.

What is congruence in Triangle?

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

Given that:

∠P ≅ ∠Q and Line Segment RS bisects ∠PQR.

In ΔPRS≅QRS ,

∠P≅∠Q (Given)

∠PRS≅∠QRS (Definition of angle bisector)

RS≅RS (reflexive property of congruence)

so,ΔPRS≅QRS (By AAS congruence)

Therefore, by the property of (Angle-Angle-Side)AAS postulates ΔPRS≅QRS

Learn more about the congruence in triangle here:

https://brainly.com/question/27085416

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