Answer:
See below
Explanation:
Given ∆PQM and ∆PRM, where M is the center of the circle and PQ = PR, we can demonstrate that ∆PQM ≡ ∆PRM by establishing that they share two pairs of congruent sides and one pair of congruent angles.
1. Congruent Sides:
a. MQ = MR:
Since M is the center of the circle, it is equidistant from all points on the circumference. Therefore, MQ = MR.
b. PQ = PR:
This is given in the problem statement.
2. Congruent Angles:
a. ∠PQM = ∠PRM:
Since MQ = MR, the radii extending from M to P and Q are congruent. This implies that ∠PQM and ∠PRM are congruent, as they are subtended by equal arcs on the same circle.
Given that ∆PQM shares two pairs of congruent sides (MQ = MR and PQ = PR) and one pair of congruent angles (∠PQM = ∠PRM), we can conclude that ∆PQM ≡ ∆PRM by the SSS Congruence Theorem.