Question

consider the diagram. the congruence theorem that can be used to prove △lon ≅ △lmn is sss. asa. sas. hl.

Explanation:

Step1: Identify common side

LN is common to both $\triangle LON$ and $\triangle LMN$.

Step2: Observe equal - length markings

From the diagram, we can see that $LO = LM$ (marked with single - hash marks) and $ON=MN$ (marked with double - hash marks).

Step3: Recall congruence theorems

SSS (Side - Side - Side) congruence theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent. Here, $LO = LM$, $ON = MN$ and $LN=LN$.

Answer:

SSS.