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.

To prove ( \triangle BIG \cong \triangle COW ) using the AAS (Angle-Angle-Side) Congruence Theorem, we need to establish that two angles and the included side of one triangle are congruent to two angles and the included side of the other triangle.

Given the congruent angles marked with single and double arcs in the triangles, we can deduce that:

1. ( \angle B \cong \angle C ) (one pair of corresponding angles)
2. ( \angle I \cong \angle O ) (the second pair of corresponding angles)
3. We also need one side to be congruent to the corresponding side. The included side must be between the two angles we already have congruent.

Thus, the triangle congruence statement must include a pair of corresponding sides.

Since we are proving to use AAS and knowing that already we have (\angle I \cong \angle O) is one pair of angles, we need another side or the other angle which we have or represent the side across.

Therefore, the best response here to prove ( \triangle BIG \cong \triangle COW ) by including the necessary information would be:

( \text{(not direct, but needs clear defining)} ) We could use ( BI \cong CO ) as the included sides (that corresponds to the angle and joins the angle pairs) to complete our AAS theorem requirements.

Among the options given, we see no direct and correct options, but ensure that's ( BI \cong CO )`:

• Correct Answer: BI¯¯¯¯¯¯≅CO¯¯¯¯¯¯¯¯