Question

PRS is isosceles with RP RS RQ is drawn such that it bisects PRS What additional fact can be used to prove PRQ SRQ by Sas in order to state that P S because they are congruent parts of congruent triangles? RQ /PS RQ /RQ PQR /SQR PQ /SQ

Answer 1

Answer:

$\frac{PQR}{SQR}$

Step-by-step explanation:

An isosceles triangle has two equal sides and the two opposite angles to the sides to be equal.

Given that; RP = RS, RQ and PS are common,

RP = SQ (opposite sides of parallelogram RPQS)

PQ = RS (opposite sides of parallelogram RPQS)

ΔRPS = ΔQPS (congruence property)

Thus comparing triangles PQR and SQR,

$\frac{PQ}{SQ}$ = $\frac{PR}{SR}$ (similarity property)

<PRS = <PRQ + <SRQ (bisection of included <PRS)

<PQS = <PQR + <SQR (similatity property to <PRS)

$\frac{PRQ}{SRQ}$  = $\frac{SQR}{PQR}$ (congruence property)

But, SRQ = PQR

So that;

       $\frac{PRQ}{SQR}$

Therefore by Side-Angle-Side (SAS), the required additional fact is:  $\frac{PRQ}{SQR}$