156k views
5 votes
Given PQM and PRM. M is the center of the circle and PQ = PR

Provide with reasons that PQM = PRM

Given PQM and PRM. M is the center of the circle and PQ = PR Provide with reasons-example-1
User Wio
by
7.8k points

1 Answer

3 votes

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.

User AlexDrenea
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories