The AAS Congruence Theorem Quick Check

Question

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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

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

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

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

BI¯¯¯¯¯¯≅CO¯¯¯¯¯¯¯¯
Modifying above upper B upper I with bar congruent to Modifying above upper C upper O with bar
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Answer 1

To prove that ΔBIG ≅ ΔCOW using the AAS (Angle-Angle-Side) Congruence Theorem, you need two pairs of angles and a pair of non-included sides that are congruent between the two triangles.

Since the question indicates that the congruence of angles has been established (with single and double arcs marking congruent angles), we know that:

• ∠B and ∠C are congruent (marked with the same arc type).
• ∠I and ∠O are congruent (which is the information we need).

So, for ΔBIG to be congruent to ΔCOW by AAS, we need confirmation of a side.

Given the options, the correct response would be:

∠I≅∠O

This indicates that angle I is congruent to angle O, which, together with the two existing congruent angles from the AAS theorem, confirms the congruence of the two triangles.