Question

in the diagram, △tjm ≅ △phs complete the following
mt =
jm =
∠p =
∠p ≅
∠m =
△hps ≅

Explanation:

Step1: Use angle - congruence property of congruent triangles

Since \(\triangle TJM\cong\triangle PHS\), corresponding angles are equal. \(\angle M\) corresponds to \(\angle S\). In \(\triangle TJM\), we know two angles: \(\angle T = 73^{\circ}\) and \(\angle J = 48^{\circ}\). Using the angle - sum property of a triangle (\(\angle T+\angle J+\angle M=180^{\circ}\)), we can find \(\angle M\).
\[m\angle M=180^{\circ}-(73^{\circ} + 48^{\circ})=59^{\circ}\]
So \(m\angle M = 59^{\circ}\) and since \(\triangle TJM\cong\triangle PHS\), \(m\angle P=m\angle T = 73^{\circ}\)

Step2: Use side - congruence property of congruent triangles

Corresponding sides of congruent triangles are equal. If \(\triangle TJM\cong\triangle PHS\), then \(\overline{JM}\cong\overline{HS}\), \(\overline{MT}\cong\overline{SP}\), \(\overline{TJ}\cong\overline{PH}\)

Answer:

\(m\angle M = 59^{\circ}\), \(m\angle P = 73^{\circ}\), \(\overline{JM}\cong\overline{HS}\), \(\overline{MT}\cong\overline{SP}\), \(\angle P\cong\angle T\)