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Triangle PRS is isosceles with RP = RS. Line RQ is drawn such that it bisects ∠PRS.

What additional fact can be used to prove that △PRQ ≅ △SRQ by SAS (Side-Angle-Side)?

A. RQ = PS
B. RQ = RQ (Reflexive Property)
C. ∠PQR = ∠SQR
D. PQ = SQ

Answer :

Answer:

PQR=SQR

Step-by-step explanation:

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Rewritten by : Barada

Answer:

[tex]\frac{PQR}{SQR}[/tex]

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,

[tex]\frac{PQ}{SQ}[/tex] = [tex]\frac{PR}{SR}[/tex] (similarity property)

[tex]\frac{PRQ}{SRQ}[/tex] = [tex]\frac{SQR}{PQR}[/tex] (congruence property)

But, SRQ = PQR

So that;

[tex]\frac{PRQ}{SQR}[/tex]

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