Question

1. if l is the midpoint of \\(\overline{kn}\\) and \\(\overline{mp}\\), which method can be used to prove the triangles are congruent?

a. side-side-side
b. side-angle-side
c. angle-side-angle
d. angle-angle-side

Explanation:

1. Since \( L \) is the midpoint of \( \overline{KN} \) and \( \overline{MP} \), we have \( KL = LN \) and \( ML = LP \) (by the definition of a midpoint, which divides a segment into two equal parts).
2. The vertical angles \( \angle KLM \) and \( \angle NLP \) are congruent (vertical angles are always congruent).
3. Now, in triangles \( \triangle KLM \) and \( \triangle NLP \), we have two sides and the included angle equal: \( KL = LN \), \( \angle KLM=\angle NLP \), and \( ML = LP \). This matches the Side - Angle - Side (SAS) congruence criterion.

Answer:

B. Side - Angle - Side