Question

1. which postulate or theorem can be used to prove that \\( \triangle mon \cong \triangle kln \\) if \\( \overline{mo} \parallel \overline{lk} \\)?

a. aas
b. hl
c. sas
d. sss
e. none of these

Explanation:

Step1: Analyze the parallel lines

Since \( \overline{MO}\parallel\overline{LK} \), by the alternate - interior angles theorem, \( \angle OMN=\angle LKN \) and \( \angle MON=\angle KLN \).

Step2: Analyze the given equal sides

We are given that \( \overline{MN}=\overline{KN} \).

Step3: Apply the AAS (Angle - Angle - Side) criterion

In \( \triangle MON \) and \( \triangle KLN \), we have two pairs of equal angles (\( \angle OMN=\angle LKN \), \( \angle MON=\angle KLN \)) and a pair of equal non - included sides (\( \overline{MN}=\overline{KN} \)). The AAS (Angle - Angle - Side) congruence criterion states that if two angles and a non - included side of one triangle are equal to the corresponding two angles and non - included side of another triangle, then the two triangles are congruent.

Answer:

A. AAS