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The AAS Congruence Theorem Quick Check
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Two triangles are next to each other: upper B upper I upper G and upper C upper O upper W. Single and double arcs are used to indicate congruent angles.

Using the AAS Congruence Theorem, what other information proves ΔBIG≅ΔCOW?

(1 point)
Responses which answer can you check it is correct and why

GB¯¯¯¯¯¯¯¯≅WC¯¯¯¯¯¯¯¯¯
Modifying above upper G upper B with bar congruent to Modifying above upper W upper C with bar

∠I≅∠O
angle upper I congruent to angle upper O

BG¯¯¯¯¯¯¯¯≅CW¯¯¯¯¯¯¯¯¯
Modifying above upper B upper G with bar congruent to Modifying above upper C upper W with bar

BI¯¯¯¯¯¯≅CO¯¯¯¯¯¯¯¯
Modifying above upper B upper I with bar congruent to Modifying above upper C upper O with bar
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Answers

Answered by GPT-4o mini
To use the AAS (Angle-Angle-Side) Congruence Theorem, we need to confirm that two angles and the included side of one triangle are congruent to the corresponding angles and included side of another triangle.

In this case, since you already have two pairs of congruent angles (indicated by the arcs), you need to provide information about one of the sides in each triangle.

Looking at the responses provided:

1. **GB ≅ WC** - This would indicate that side GB in triangle BIG is congruent to side WC in triangle COW. Although this provides relevant information, it does not directly relate to the AAS condition.

2. **∠I ≅ ∠O** - This reinforces that the angles are congruent but does not provide information about a side.

3. **BG ≅ CW** - This comparison of sides could be useful, but it is not directly useful for establishing congruence through AAS since you need to relate the triangles through the corresponding sides in relation to the angles provided.

4. **BI ≅ CO** - This would show that the side BI in triangle BIG is congruent to the side CO in triangle COW, contributing to establishing the AAS congruence condition since we already have two pairs of congruent angles.

Given the AAS theorem and the fact that two pairs of angles are already congruent, the best choice would be:

**BI ≅ CO**

This confirms the condition of the AAS theorem that we have two angles and the included side between them is also congruent.

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