Question

△vwy≅△xuy. complete the proof that △wxy≅△uvy.
statement
1 △vwy≅△xuy
2 uy≅wy
3 vy≅xy
4 ∠uyv≅∠wyx
5
reason
given
cpctc
cpctc
vertical angle theorem

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Identify the sides and angle for \(\triangle WXY\) and \(\triangle UVY\)

We know from steps 2 and 3 that \( \overline{UY}\cong\overline{WY}\), \( \overline{VY}\cong\overline{XY}\), and from step 4 that \( \angle UYV\cong\angle WYX\)

Step3: Apply the SAS congruence criterion

Since in \(\triangle WXY\) and \(\triangle UVY\), we have \( \overline{UY}\cong\overline{WY}\), \( \angle UYV\cong\angle WYX\), \( \overline{VY}\cong\overline{XY}\)

Answer:

\(\triangle WXY\cong\triangle UVY\) (by SAS congruence criterion)