Additional Information for Triangle Congruence Proof

In the diagram below, is the midpoint of line segment

.

In order to prove that are congruent by the triangle congruence theorem, what additional information is needed? (Write your answer using geometric notation)

To prove that triangles ( \triangle ABC ) and ( \triangle A'B'C' ) are congruent by the triangle congruence theorem, we need to establish that they satisfy one of the congruence criteria (such as SSS, SAS, ASA, AAS, or HL).

Assuming that ( M ) is the midpoint of line segment ( AB ), we can state that ( AM \cong MB ).

To complete the proof of congruence, we need additional information. One possible option could be:

• ( AC \cong A'C' ) (corresponding sides are congruent).

This would allow us to use the Side-Side-Side (SSS) congruence theorem to conclude that ( \triangle ABC \cong \triangle A'B'C' ).

Alternatively, if we have information about angles, we could state:

• ( \angle A \cong \angle A' ) and ( \angle B \cong \angle B' ) (corresponding angles are congruent).

This would allow us to use the Angle-Side-Angle (ASA) congruence theorem.

In summary, the additional information needed could be:

1. ( AC \cong A'C' ) (for SSS), or
2. ( \angle A \cong \angle A' ) and ( \angle B \cong \angle B' ) (for ASA).

Please specify which additional information you would like to use for the proof.