Question

complete the proof that $\triangle wxy\cong\triangle wyx$.

1 $\overline{wx}\cong\overline{wy}$ given
2 $\angle w\cong\angle w$
3 $\triangle wxy\cong\triangle wyx$

Explanation:

Step1: Reason for ∠W ≅ ∠W

Reflexive property of congruence (an angle is congruent to itself).

Step2: Reason for △WXY ≅ △WYX

Side - Angle - Side (SAS) congruence criterion. Since \( \overline{WX}\cong\overline{WY}\) (given), \( \angle W\cong\angle W\) (reflexive property), and \( \overline{WZ}\) (common side, but in the triangles \( \triangle WXY\) and \( \triangle WYX\), the sides \( \overline{WX}\) and \( \overline{WY}\), the included angle \( \angle W\) satisfy the SAS condition).

Answer:

1. Reflexive property of congruence; 3. SAS (Side - Angle - Side) congruence criterion.