Question

z is the midpoint of ( overline{xy} ) and ( overline{wz} perp overline{xy} ). complete the proof that ( \triangle wxz cong \triangle wyz ).

Explanation:

Step1: Identify the common side

$\overline{WZ}\cong\overline{WZ}$ (Reflexive property of congruence)

Step2: Apply the SAS (Side - Angle - Side) congruence criterion

In $\triangle WXZ$ and $\triangle WYZ$, we have $\overline{XZ}\cong\overline{YZ}$ (from step 4 in the given proof, definition of mid - point), $\angle WZX\cong\angle WZY$ (from step 3, all right angles are congruent), and $\overline{WZ}\cong\overline{WZ}$ (reflexive property). So, $\triangle WXZ\cong\triangle WYZ$ (by SAS congruence criterion)

Answer:

$\triangle WXZ\cong\triangle WYZ$; SAS (Side - Angle - Side) congruence criterion