Question

xy ≅ vw and wx ≅ vy. complete the proof that △vwx ≅ △xyv.

1 xy ≅ vw
2 wx ≅ vy
3 vx ≅ vx
4 △vwx ≅ △xyv

Explanation:

Step1: Given

$\overline{XY}\cong\overline{VW}$ is given in the problem statement.

Step2: Given

$\overline{WX}\cong\overline{VY}$ is given in the problem statement.

Step3: Reflexive property of congruence

For any segment $\overline{a}$, $\overline{a}\cong\overline{a}$. So, $\overline{VX}\cong\overline{VX}$.

Step4: 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. Since $\overline{XY}\cong\overline{VW}$, $\overline{WX}\cong\overline{VY}$ and $\overline{VX}\cong\overline{VX}$, by SSS, $\triangle VWX\cong\triangle XYV$.

Answer:

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