Question

Use the image to answer the question. Using the AAS Congruence Theorem, what other information proves ΔBIG≅ΔCOW? (1 point) Responses ∠I≅∠O angle upper I congruent to angle upper O 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 BI¯¯¯¯¯¯≅CO¯¯¯¯¯¯¯¯

Answer 1

To determine congruence between triangles ΔBIG and ΔCOW using the AAS (Angle-Angle-Side) Congruence Theorem, we need two angles and the non-included side of one triangle to be congruent to the corresponding parts of the other triangle.

You mentioned three pairs of congruent segments and angles:

1. ∠I ≅ ∠O
2. GB̅̅̅̅̅̅ ≅ WC̅̅̅̅̅̅
3. BG̅̅̅̅̅̅ ≅ CW̅̅̅̅̅̅

Given this information, you can prove ΔBIG ≅ ΔCOW using AAS if you also know:

• Two angles are congruent: ∠I ≅ ∠O.
• One side, which is not between these two angles, is also congruent: for instance, GB̅̅̅̅̅̅ ≅ WC̅̅̅̅̅̅.

Thus, the sufficient information to apply the AAS Congruence Theorem for ΔBIG and ΔCOW is:

Option: ∠I ≅ ∠O (one angle congruence) and GB̅̅̅̅̅̅ ≅ WC̅̅̅̅̅̅ (side congruence).

With these two pieces of congruent information, along with the fact that you also have another pair of angles, the statement concludes that ΔBIG ≅ ΔCOW.