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

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}
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Solution

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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".

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