Question

given mp = mq and pr = qr, select the two true statements that are used to prove that mr bisects ∠lmn. ∠pmr≅∠qmr because corresponding parts of congruent triangles are congruent △pmr≅△qmr by the side - side - side criterion △mpq≅△prq by the side - side - side criterion lm = mn because corresponding parts of congruent triangles are congruent pr⊥qr because p and q are equidistant from mr

Explanation:

Step1: Identify congruent triangles

We know that \(MP = MQ\) and \(PR=QR\), and \(MR = MR\) (common - side). So, by the side - side - side (SSS) criterion, \(\triangle PMR\cong\triangle QMR\).

Step2: Use corresponding parts of congruent triangles

If \(\triangle PMR\cong\triangle QMR\), then corresponding parts of congruent triangles are congruent. So, \(\angle PMR\cong\angle QMR\), which means \(MR\) bisects \(\angle LMN\).

Answer:

1. \(\triangle PMR\cong\triangle QMR\) by the side - side - side criterion
2. \(\angle PMR\cong\angle QMR\) because corresponding parts of congruent triangles are congruent