Question

consider the diagram.
the congruence theorem that can be used to prove $\triangle lon \cong \triangle lmn$ is
\\( \bigcirc \\) sss,
\\( \bigcirc \\) asa,
\\( \bigcirc \\) sas,
\\( \bigcirc \\) hl.

Explanation:

Step1: Identify common side

In \(\triangle LON\) and \(\triangle LMN\), \(LN = LN\) (common side).

Step2: Analyze given equal sides

From the diagram, \(OL = ML\) and \(ON = MN\).

Step3: Apply congruence theorem

Since three pairs of corresponding sides are equal (\(OL = ML\), \(ON = MN\), \(LN = LN\)), by the SSS (Side - Side - Side) congruence theorem, \(\triangle LON\cong\triangle LMN\).

Answer:

SSS.