Question

complete the proof that \\( \triangle vwx \cong \triangle vyx \\).

Explanation:

Step1: Identify the reason for \(\overline{VY}\cong\overline{VW}\)

Given (as marked in the figure).

Step2: Identify the reason for \(\overline{WX}\cong\overline{XY}\)

Given (as marked in the figure).

Step3: Identify the reason for \(\overline{VX}\cong\overline{VX}\)

Reflexive property of congruence (a segment is congruent to itself).

Step4: Identify the reason for \(\triangle VWX\cong\triangle VYX\)

SSS (Side - Side - Side) congruence criterion (if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent).

Answer:

1. Given
2. Given
3. Reflexive property of congruence
4. SSS (Side - Side - Side) congruence criterion