Question

activity 1: which triangles are congruent?
here are 3 triangles.

1. triangle ( pqr ) is congruent to which triangle? explain your reasoning.

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

Two triangles are congruent by SAS if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Step2: Analyze triangle \(PQR\) and triangle \(NML\)

In \(\triangle PQR\), we have \(PQ = 5.9\), \(\angle Q=46.6^{\circ}\), \(QR = 4.3\).
In \(\triangle NML\), we have \(NM = 5.9\), \(\angle M = 46.6^{\circ}\), \(ML=4.3\).
The sides \(PQ\) and \(NM\) are equal (\(PQ = NM = 5.9\)), the included angles \(\angle Q\) and \(\angle M\) are equal (\(\angle Q=\angle M = 46.6^{\circ}\)), and the sides \(QR\) and \(ML\) are equal (\(QR = ML = 4.3\)).

Answer:

Triangle \(PQR\) is congruent to triangle \(NML\) by the SAS (Side - Angle - Side) congruence criterion.