Question

w is the midpoint of \\( \overline { v x } \\), \\( \overline { x z } \cong \overline { v y } \\), and \\( \overline { w z } \cong \overline { w y } \\). complete the proof that \\( \triangle v w y \cong \triangle x w z \\).

Explanation:

Step1: Given

Statement 1 is given in the problem.

Step2: Given

Statement 2 is given in the problem.

Step3: Given

Statement 3 is given in the problem.

Step4: Definition of midpoint

Since \(W\) is the midpoint of \(\overline{VX}\), by the definition of a midpoint, \(VW = WX\), so \(\overline{VW}\cong\overline{WX}\).

Step5: SSS (Side - Side - Side) Congruence Theorem

We have \(\overline{VW}\cong\overline{WX}\) (from step 4), \(\overline{XZ}\cong\overline{VY}\) (from step 2), and \(\overline{WZ}\cong\overline{WY}\) (from step 3). So, by the SSS (Side - Side - Side) congruence theorem, \(\triangle VWY\cong\triangle XWZ\).

Answer:

1. Given
2. Given
3. Given
4. Definition of midpoint
5. SSS (Side - Side - Side) Congruence Theorem