Question

are the triangles congruent? if so, write a congruence statement and reason why.
(1 point)
yes, △abc ≅ △mln by the sss congruence theorem.
no, the triangles are not congruent
yes, △abc ≅ △lnm by the sss congruence theorem
yes, △abc ≅ △lmn by the sss congruence theorem

Explanation:

Step1: Check SSS Congruence

SSS (Side - Side - Side) Congruence Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.
In \(\triangle ABC\) and \(\triangle LMN\), \(AB = LM\) (one mark), \(BC=LN\) (two marks), \(AC = MN\) (three marks).

Step2: Match Vertices

When writing the congruence statement, vertices must be in corresponding order. \(A\) corresponds to \(L\), \(B\) corresponds to \(M\), \(C\) corresponds to \(N\).

Answer:

Yes, \(\triangle ABC\cong\triangle LMN\) by the SSS Congruence Theorem.