Questions: Proving triangles congruent by SSS and SAS VVZ
YZ ≅ XZ and VZ ≅ WZ. Complete the proof that triangle VYZ ≅ triangle WXZ.
Statement Reason
--- ---
1 YZ ≅ XZ Given
2 VZ ≅ WZ Given
3 angle VZY ≅ angle WZX
4 triangle WZ ≅ triangle WXZ
Transcript text: Proving triangles congruent by SSS and SAS VVZ
$\overline{Y Z} \cong \overline{X Z}$ and $\overline{V Z} \cong \overline{W Z}$. Complete the proof that $\triangle V Y Z \cong \triangle W X Z$.
\begin{tabular}{|l|l|l|}
\hline & Statement & Reason \\
\hline 1 & $\overline{Y Z} \cong \overline{X Z}$ & Given \\
\hline 2 & $\overline{V Z} \cong \overline{W Z}$ & Given \\
\hline 3 & $\angle V Z Y \cong \angle W Z X$ & \\
\hline 4 & $\Delta W Z \cong \Delta W X Z$ & \\
\hline
\end{tabular}
Solution
Solution Steps
Step 1: Identify the givens
We are given that YZ ≅ XZ and VZ ≅ WZ. We are also given that ∠VZY ≅ ∠WXZ.
Step 2: Determine the congruency theorem
We have two pairs of congruent sides and a pair of congruent angles. Since the congruent angles are between the pairs of congruent sides (Side-Angle-Side), we can use the SAS Congruence Postulate.
Step 3: Complete the proof
The missing reason in step 3 is Vertical Angles are Congruent. Because all three corresponding sides and all three corresponding angles are congruent, triangle VYZ is congruent to triangle WXZ by SAS.
Final Answer:
The reason for step 3 is "Vertical Angles are Congruent". The reason for step 4 is "SAS".