Question

directions: for each triangle pair drawn, write the parts and pieces you know to be congruent. if there is enough information for proof, write a triangle congruence statement and the theorem that proves the two triangles are congruent. given ( overline{wy} ) bisects ( angle zwx ) and ( overline{zw} cong overline{wx} ) the triangles congruent, by , so ( \triangle wyz cong \triangle )

Explanation:

Step1: Identify congruent parts from the given information

Since \(WY\) bisects \(\angle ZWX\), we have \(\angle ZWY=\angle XWY\). Given \(ZW\cong WX\), and \(WY = WY\) (common side).

Step2: Apply the congruence theorem

In \(\triangle WYZ\) and \(\triangle WYX\), we have \(ZW\cong WX\), \(\angle ZWY\cong\angle XWY\), \(WY\cong WY\). By the Side - Angle - Side (SAS) congruence theorem.

Answer:

The triangles are congruent, by SAS, so \(\triangle WYZ\cong\triangle WYX\)