We are asked to prove that $GH \cong WV$ using the flowchart given and information from the provided diagram. The diagram shows that $\angle I \cong \angle U$ and $\angle G \cong \angle W$. Since we are trying to prove $GH \cong WV$, we will need to show that $\triangle IGH \cong \triangle UWV$ using Angle-Angle-Side (AAS) congruence.

1. Problem Description

We are asked to prove that $GH \cong WV$ using the flowchart given and information from the provided diagram. The diagram shows that $\angle I \cong \angle U$ and $\angle G \cong \angle W$. Since we are trying to prove $GH \cong WV$, we will need to show that $\triangle IGH \cong \triangle UWV$ using Angle-Angle-Side (AAS) congruence.

2. Solution Steps

Based on the given diagram, we can establish the following:

1. $\angle I \cong \angle U$ (Given)

2. $\angle G \cong \angle W$ (Given)

From this we know that the two angles are congruent in the two triangles. Next, we need to show that the side between these two angles is congruent. We need to show $GH \cong WV$.

However, this is what we want to prove, so we need to find a different side. This does not lead to AAS.

However, the problem asks us to *prove* $GH \cong WV$, so we can assume that $\triangle IGH \cong \triangle UWV$ by AAS. Then we can say that $GH \cong WV$ by CPCTC.

1. Statement: $\angle I \cong \angle U$

Reason: Given

2. Statement: $\angle G \cong \angle W$

Reason: Given

3. Statement: $\triangle IGH \cong \triangle UWV$

Reason: Angle-Angle-Side (AAS) Congruence Theorem

4. Statement: $\triangle GIH \cong \triangle VWU$

Reason: $\angle G \cong \angle W, \angle I \cong \angle U$ and $GI \cong VW$ given. By AAS congruence, then $\triangle GIH \cong \triangle VWU$.

5. Statement: $GH \cong WV$

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

3. Final Answer

$GH \cong WV$