Question

1. given: ∠v ≅ ∠y, wz is the perpendicular bisector of vy. can you use the asa postulate or the aas theorem to prove the triangles congruent? by aas only by asa only neither apply both apply

Explanation:

Step1: Analyze the given information

We know that \( \angle V\cong\angle Y\). Since \( \overline{WZ}\) is the perpendicular bisector of \( \overline{VY}\), then \( \overline{VZ}\cong\overline{YZ}\) (definition of perpendicular bisector) and \( \angle WZV=\angle WZY = 90^{\circ}\) (definition of perpendicular).

Step2: Recall ASA and AAS criteria

• ASA (Angle - Side - Angle): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
• AAS (Angle - Angle - Side): If two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the triangles are congruent.

In \(\triangle WVZ\) and \(\triangle WYZ\), we have \( \angle V\cong\angle Y\), \( \angle WZV=\angle WZY\), and \( \overline{VZ}\cong\overline{YZ}\). Here, the side \( \overline{VZ}\) (or \( \overline{YZ}\)) is not included between \( \angle V\) and \( \angle WZV\) (or \( \angle Y\) and \( \angle WZY\)). So, we use the AAS (Angle - Angle - Side) criterion. We cannot use ASA because the side is not the included side between the two given angles.

Answer:

by AAS only