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 $\triangle LMN$. So, $LN = LN$.

Step2: Use given equal sides

From the diagram, $LO = LM$ (marked with one tick) and $ON = MN$ (marked with two ticks).

Step3: Apply SSS congruence

Since $LO = LM$, $ON = MN$, and $LN = LN$, by the SSS (Side - Side - Side) congruence theorem, $\triangle LON\cong\triangle LMN$.

Answer:

SSS.