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:
- ( AC \cong A'C' ) (for SSS), or
- ( \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.