Question

δwxz ≅ δyvz. complete the proof that \overline{vw} ≅ \overline{xy}.

Explanation:

Step1: Given

$\triangle WXZ\cong\triangle YVZ$ (Given)

Step2: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

Since $\triangle WXZ\cong\triangle YVZ$, then $\overline{VZ}\cong\overline{XZ}$ (CPCTC), $\overline{WZ}\cong\overline{YZ}$ (CPCTC)

Step3: Vertical Angles Theorem

$\angle VZW\cong\angle XZY$ (Vertical Angles Theorem)

Step4: SAS (Side - Angle - Side) Congruence Criterion

In $\triangle XYZ$ and $\triangle VWZ$, we have $\overline{VZ}\cong\overline{XZ}$, $\angle VZW\cong\angle XZY$, $\overline{WZ}\cong\overline{YZ}$. So, $\triangle XYZ\cong\triangle VWZ$ (SAS)

Step5: CPCTC

Since $\triangle XYZ\cong\triangle VWZ$, then $\overline{VW}\cong\overline{XY}$ (CPCTC)

Answer:

1. Given
2. CPCTC
3. CPCTC
4. Vertical Angles Theorem
5. SAS
6. CPCTC