Question

question 10 of 10
tyrell is going to use asa to prove that ( \triangle pqrcong\triangle sqr ).
which of these is a necessary step in tyrells proof?
a. prove that ( overline{qr}congoverline{qr} ) by the reflexive property.
b. prove that ( angle qprcongangle qsr ) by the symmetric property.
c. prove that ( overline{pq}congoverline{sq} ) by the reflexive property.
d. prove that ( angle pqrcongangle sqr ) by the symmetric property.

Explanation:

• The ASA (Angle - Side - Angle) congruence criterion requires two angles and the included side to be congruent.
• In \(\triangle PQR\) and \(\triangle SQR\), we already have \(\angle PRQ=\angle SRQ = 90^{\circ}\) (right angles) and the given equal angles at \(Q\).
• The side \(QR\) is common to both triangles. By the reflexive property of congruence (\(a=a\)), we need to establish that \(\overline{QR}\cong\overline{QR}\) as it is the included side for the two pairs of angles.

Answer:

A. Prove that \(\overline{QR}\cong\overline{QR}\) by the reflexive property.