In triangles ABC and LMN, ∠A ≅ ∠L, ∠B ≅ ∠M, and ∠C ≅ ∠N. Is this information sufficient to prove triangles ABC and LMN congruent through ASA? Explain your answer.

(see below)

Step-by-step explanation:

No, this is not enough info.

Why?

All three angles may be congruent, but this doesn't prove that the sides are also congruent to each other. For instance, the angles may have the same measures but the sides may not. See the attached image for more specifics.

The only way you can tell two triangles are congruent when given congruence statement are these three triangle congruence theorems:

SSS (side-side-side) Theorem—if all three sides of both triangles are congruent, then the two triangles are congruent.

ASA (angle-side-angle) Theorem—if two corresponding angles and their attaching side of both triangles are congruent, then the two triangles are congruent.

SAS (side-angle-side) Theorem—if two corresponding sides and the included angle of two triangles are congruent, then the two triangles are congruent.

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