Question

based on the information provided, determine whether a congruence exists between the two triangles. if a congruence exists between the triangles, state the congruencies and the criteria used to determine them. given: m is the mid - point of hp, m∠h=m∠p

Explanation:

Step1: Recall mid - point property

Since \(M\) is the mid - point of \(HP\), we have \(HM = MP\).

Step2: Identify vertical angles

\(\angle HMG\) and \(\angle PMR\) are vertical angles, so \(\angle HMG=\angle PMR\).

Step3: Check for congruence criteria

We are given \(\angle H=\angle P\), and we have \(HM = MP\) and \(\angle HMG=\angle PMR\). By the Angle - Side - Angle (ASA) congruence criterion, \(\triangle HMG\cong\triangle PMR\).

Answer:

\(\triangle HMG\cong\triangle PMR\) by ASA criterion.