Question

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

Explanation:

To determine the congruence theorem for \(\triangle LON \cong \triangle LMN\), we analyze the diagram (assuming it's a rhombus or a figure with \(LO = LM\), \(ON = MN\), and \(LN\) as a common side).

• \(LO = LM\) (sides of the figure, likely equal).
• \(ON = MN\) (sides of the figure, likely equal).
• \(LN\) is common to both triangles, so \(LN = LN\).

By the SSS (Side - Side - Side) congruence theorem, if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. Here, all three corresponding sides (\(LO = LM\), \(ON = MN\), \(LN = LN\)) are equal, so SSS applies. ASA requires two angles and the included side, SAS requires two sides and the included angle, and HL is for right - angled triangles (no indication of right angles here).

Answer:

SSS