Question

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

Explanation:

Step1: Prove triangles congruent

Since \(\overline{LM}\cong\overline{NM}\), \(\overline{LO}\cong\overline{NO}\), and \(\overline{MO}\cong\overline{MO}\) (common side), by SSS (Side - Side - Side) congruence criterion, \(\triangle LMO\cong\triangle NMO\).

Step2: Use congruent triangles property

Corresponding parts of congruent triangles are equal. So, \(\angle LMO\cong\angle NMO\). Also, \(\angle LMO+\angle NMO = 180^{\circ}\) (linear pair). Then \(2\angle LMO=180^{\circ}\), so \(\angle LMO = 90^{\circ}\) and \(\angle NMO=90^{\circ}\). Thus, \(\overline{LN}\perp\overline{MO}\).

Answer:

A. True