Question

complete the proof that \\( \triangle vwy \cong \triangle uxy \\).

Explanation:

Step1: Identify the reason for $\overline{VY}\cong\overline{UY}$

From the figure, we can see that it is given (marked with one - tick mark).

Step2: Identify the reason for $\overline{XY}\cong\overline{WY}$

From the figure, we can see that it is given (marked with two - tick marks).

Step3: Identify the reason for $\angle UYX\cong\angle VWY$

Vertical angles are congruent. $\angle UYX$ and $\angle VWY$ are vertical angles.

Step4: Identify the reason for $\triangle VWY\cong\triangle UXY$

We have two sides and the included angle congruent. By the Side - Angle - Side (SAS) congruence criterion, $\triangle VWY\cong\triangle UXY$.

Answer:

1. Given
2. Given
3. Vertical angles are congruent
4. SAS (Side - Angle - Side) congruence criterion