Question

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1. Given: ∠P ≅ ∠Q and RS bisects ∠PQR.
Prove: PR≅ QR

Supply the missing reason in Statement 2 of the proof of the the Converse of the Isosceles Triangle Theorem.

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


A)Definition of angle bisector

B)AAS Theorem

C)CPCTC

D)Reflexive Property of Congruence

Answer 1

Solution:

→In ΔP QR,∠P ≅ ∠Q and RS bisects ∠P QR.

→In ΔP Q R

∠P ≅ ∠Q  ----[Given]

PR=QR ----[If in a triangle ,two angles are equal , Side Opposite to them are equal.]

The other method is ,

Draw , RS ,which is perpendicular bisector of ∠ P R Q.

In ΔP SR and ΔQ SR

∠P ≅ ∠Q

RS is common.

2.∠PRS=∠SRQ→Definition of angle bisector.

→ΔP SR ≅ ΔQ SR-----[A AS]

PR=QR ----[CPCT]

∠PRS=∠SRQ→Definition of angle bisector.

Option A: Definition of angle bisector

Answer 2

The missing reason in Statement 2 of the proof of the the Converse of the Isosceles Triangle Theorem that ∠PRS ≅ ∠QRS is;

A: Definition of angle bisector.

What are angle proofs in a triangle?

We are given that ∠P ≅ ∠Q and RS bisects ∠PQR.

From the attached image, we can say that;

In ΔPRS ΔQRS,  SR ≅  SR Due to the theorem of reflexive property of congruence

We can say that PR = QR because of AAS congruency postulate.

Thus, we can conclude that ∠PRS ≅ ∠QRS due to the Definition of angle bisector

Read more about angle proofs in a triangle at; https://brainly.com/question/24839702