Questions: U Y ≅ U W. Complete the proof that W Z ≅ V Y. - Statement - Reason 1. ∠W ≅ ∠Y - 2. U Y ≅ U W - 3. ∠U ≅ ∠U - 4. ΔUWY ≅ ΔUZW - 5. W Z ≅ W Y -

Transcript text: $\overline{U Y} \cong \overline{U W}$. Complete the proof that $\overline{W Z} \cong \overline{V Y}$. \begin{tabular}{|l|l|l|} \hline & Statement & Reason \\ \hline 1 & $\angle W \cong \angle Y$ & $\square$ \\ 2 & $\overline{U Y} \cong \overline{U W}$ & $\square$ \\ 3 & $\angle U \cong \angle U$ & $\square$ \\ 4 & $\Delta U W Y \cong $\Delta U Z W$ & $\square$ \\ 5 & $\overline{W Z} \cong \overline{W Y}$ & $\square$ \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Angle W and Angle Y are congruent

The problem states that $\angle W \cong \angle Y$. This is given.

Step 2: Side UY and Side UW are congruent

The problem states that $\overline{UY} \cong \overline{UW}$. This is given.

Step 3: Angle U is congruent to itself

$\angle U \cong \angle U$ because of the reflexive property of congruence.

Step 4: Triangles UVY and UZW are congruent

We have two pairs of congruent angles ($\angle W \cong \angle Y$ and $\angle U \cong \angle U$) and a pair of congruent sides between those angles ($\overline{UY} \cong \overline{UW}$). Thus, by the Angle-Side-Angle (ASA) Postulate, $\triangle UVY \cong \triangle UZW$.

Step 5: Side WZ is congruent to side VY

Since $\triangle UVY \cong \triangle UZW$, corresponding parts of congruent triangles are congruent (CPCTC). Therefore, $\overline{WZ} \cong \overline{VY}$.

Final Answer:

Given
Given
Reflexive Property of Congruence
ASA Postulate
CPCTC

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