Question

hw 5: proving triangles congruent: sss & sas
state whether the triangles could be proven congruent, if possible, by sss or sas. then, write a congruency statement.
6.
the triangles ▼ congruent by ▼
△▼▼▼ ≅ △▼▼▼

Explanation:

Step1: Analyze Given Information

We have a diagram with \( \triangle WXZ \) and \( \triangle YXZ \). \( Z \) is the midpoint of \( WY \) (so \( WZ = YZ \)) and \( XZ \perp WY \) (so \( \angle WZX=\angle YZX = 90^\circ \)), and \( XZ \) is common to both triangles.

Step2: Identify Congruence Criterion

• \( WZ = YZ \) (given by the tick marks).
• \( \angle WZX=\angle YZX = 90^\circ \) (right angle).
• \( XZ = XZ \) (common side).

This satisfies the SAS (Side - Angle - Side) congruence criterion because we have two sides and the included angle equal.

Step3: Write Congruency Statement

Based on the correspondence of vertices ( \( W \) corresponds to \( Y \), \( Z \) corresponds to \( Z \), \( X \) corresponds to \( X \) ), the congruency statement is \( \triangle WXZ\cong\triangle YXZ \). Also, the triangles are congruent.

Answer:

The triangles \(\boldsymbol{\text{are}}\) congruent by \(\boldsymbol{\text{SAS}}\). The congruency statement is \(\boldsymbol{\triangle WXZ\cong\triangle YXZ}\)