Question

v. geometry sem a geometry
triangle congruence theorems
consider the diagram.
the congruence theorem that can be used to prove \\( \triangle lon \cong \triangle lmn \\) is
hl.
asa.
sss.
sas.

Explanation:

Step1: Recall triangle congruence theorems

• HL (Hypotenuse - Leg): For right - angled triangles. But there is no information about right angles in \(\triangle LON\) and \(\triangle LMN\).
• ASA (Angle - Side - Angle): Requires two angles and the included side. There is no information about angles being congruent in the given diagram.
• SSS (Side - Side - Side): If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.

From the diagram, \(LO = LM\), \(ON = MN\), and \(LN\) is common to both \(\triangle LON\) and \(\triangle LMN\). So \(LN=LN\) (reflexive property).

• SAS (Side - Angle - Side): Requires two sides and the included angle. There is no information about angles being congruent in the given diagram.

Answer:

SSS.