Question

1. in the diagram below, right triangle pqr is transformed by a sequence of rigid motions that maps it onto right triangle nml. write a set of three congruency statements that would show asa congruency for these triangles.

Explanation:

Step1: Identify corresponding angles and sides

Since the triangles are congruent by ASA (Angle - Side - Angle), we need to match the angles and the included side.
We know that \(\angle Q=\angle M = 90^{\circ}\) (right angles).
Let's assume that the side between two angles is considered. If we assume \(PQ = ML\) (the sides between the angles we will identify).

Step2: Identify another pair of angles

We can say \(\angle P=\angle L\) (by the property of congruent triangles after transformation).

Step3: Write the congruency statement

By ASA congruency criterion, \(\triangle PQR\cong\triangle MLN\) because \(\angle Q=\angle M\), \(PQ = ML\), \(\angle P=\angle L\)

Answer:

\(\angle Q=\angle M\), \(PQ = ML\), \(\angle P=\angle L\) so \(\triangle PQR\cong\triangle MLN\) by ASA