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

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

multiple all that

step-by-step explanation:

27×17