Question

Using the AAS Congruence Theorem, what other information proves ΔBIG≅ΔCOW ? (1 point) GB¯¯¯¯¯¯¯¯≅WC¯¯¯¯¯¯¯¯¯
BI¯¯¯¯¯¯≅CO¯¯¯¯¯¯¯¯
BG¯¯¯¯¯¯¯¯≅CW¯¯¯¯¯¯¯¯¯
∠I≅∠O

Answer 1

To prove that \( \Delta BIG \cong \Delta COW \) using the AAS (Angle-Angle-Side) Congruence Theorem, you need two pairs of corresponding angles and one pair of corresponding sides.

You already have:

1. \( \angle I \cong \angle O \) (one pair of corresponding angles)
2. The statement \( GB \cong WC \) (which provides a corresponding side).

To apply the AAS Theorem, we need one more pair of angles:

- You can choose either \( BI \cong CO \) or \( BG \cong CW \) to confirm the second pair of sides if we can establish a relationship between other angles.

Here’s the structure you’d need:

1. Pair of angles: \( \angle I \cong \angle O \)
2. Pair of angles: (let's say) \( \angle B \cong \angle C \) (this needs to be stated or proven based on the given diagram or context).
3. Pair of sides: \( GB \cong WC \)

If you have the second angle congruence established, you can complete the proof with:

- \( \Delta BIG \cong \Delta COW \) by AAS, because we have two pairs of angles and the non-included side.

Thus, to use AAS effectively, ensure you emphasize the congruence of another angle along with the given congruence of sides to reach the conclusion.