Final answer:
Useful information to prove Δabc is congruent to Δnml includes the congruence of two pairs of angles (∠b ≅ ∠m and ∠c ≅ ∠l) and knowledge of a translation, which preserves congruence. Right triangle status could also assist if a side length is known.
Step-by-step explanation:
To prove that Δabc is congruent to Δnml, additional information that would be useful includes angle congruences and transformations that preserve the shape and size of the triangle. The following pieces of information could be applicable:
- ∠b ≅ ∠m: Knowing two angles are congruent contributes to proving triangle congruence through angle-angle-side (AAS) or angle-side-angle (ASA) criteria.
- Δabc is a right triangle: If both triangles are right triangles, and we have one side and one right angle congruent, then by Hypotenuse-Leg (HL) congruence for right triangles, they could be proven congruent.
- Δabc was rotated and dilated by a scale factor between 0 and 1: A dilation by a scale factor other than 1 would not preserve the size of the triangle, so this transformation would not help prove congruence.
- Δabc was translated right and down: A translation preserves the shape and size of a figure so this transformation would help prove congruence.
- ∠c ≅ ∠l: Like with the first point, knowing another pair of angles are congruent helps in establishing congruence through AAS or ASA criteria.