Question

Question
Use the image to answer the question.

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

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

GB¯¯¯¯¯¯¯¯≅WC¯¯¯¯¯¯¯¯¯

Answer 1

To apply the AAS (Angle-Angle-Side) Congruence Theorem, you need two angles and the length of the side that is not included between those angles to be congruent in both triangles.

In the case of triangles ΔBIG and ΔCOW, since we have already established that the angles ∠B ≅ ∠C and ∠I ≅ ∠O are congruent (indicated by the arcs in the diagram), the additional information needed is for a side of one triangle to be congruent to a corresponding side of the other triangle.

From the options provided, the response that would help complete the proof of ΔBIG ≅ ΔCOW using the AAS theorem would be:

**BI¯¯¯¯¯¯≅CO¯¯¯¯¯¯¯¯**

This indicates that the sides BI and CO are congruent, fulfilling the AAS criteria. Therefore, with the two angles and one side congruent, we can conclude that the two triangles are indeed congruent.