Question

question 3 of 10
based only on the given information, it is guaranteed that (overline{on}perpoverline{mo}).
given: (\triangle lon)
(overline{lm}congoverline{nm})
(overline{lo}congoverline{no})
(overline{mo}congoverline{mo})
a. true
b. false

Explanation:

Step1: Check triangle congruence

Given \( \overline{LM}\cong\overline{NM}\), \( \overline{LO}\cong\overline{NO}\), \( \overline{MO}\cong\overline{MO}\). By SSS (Side - Side - Side) congruence criterion, \( \triangle LMO\cong\triangle NMO\).

Step2: Analyze angles

Since \( \triangle LMO\cong\triangle NMO\), \( \angle LMO\cong\angle NMO\). Also, \( \angle LMO+\angle NMO = 180^{\circ}\) (linear pair). So \( \angle LMO=\angle NMO = 90^{\circ}\), which means \( \overline{MO}\perp\overline{LN}\).

Answer:

A. True