Question

RS2. Given: ZP ZQ andProve: PR=QRSupply the missing reason in Statement 1 of the proof of the the Converse of the Isosceles Triangle Theorem.Begin with isosceles APRQ with ZP ZQ. Construct RS, a bisector of ZPRQ.bisects ZPQR.R

Answer 1

We are given the following triangle:

We are given that:

$\angle P=\angle Q$

Since RS is a bisector this means that:

$\angle PRS=\angle SRQ$

Also, since S is a midpoint of PQ:

$PS=SQ$

By the reflexive property we have:

$RS=RS$

Since we have two pairs of congruent angles this means that:

$\angle PSR=\angle QSR$

Therefore, by SAS theorem of congruency:

$\Delta PSR\cong\Delta QSR$

Since the triangles are congruent this means that all of its sides are congruent too, therefore:

$PR=QR$

And thus we have concluded the proof.