Question

The figure below shows segments KL and MN which intersect at point P. Segment KM is parallel to segment LN.

Which of these facts is used to prove that triangle KMP is similar to triangle LNP?

A)Angle KMP is congruent to angle LPN.
B)Angle KMP is congruent to angle LNP.
C)Angle KPM is congruent to angle PLN.
D)Angle KPM is congruent to angle LNP.

Answer 1

The correct answer should be Angle KMP is congruent to angle LNP

Explanation:

In the question we are told that KM is congruent to LN so it wouldn't make sense to seperate KM and LN.

Answer 2

A)Angle KMP is congruent to angle LPN.

Explanation:

Knowing that KM and NL are parallel, angle KMP and LNP would be alternate interior angles, as they are inside the parallel lines and on the opposite side of NM, the transversal. We know that alternate interior angles are congruent.

We also know that angle KPM and LPN are congruent, as they are vertical angles (opposite angles that share only a vertex). This gives us two angles congruent, which is what we need for the AA similarity postulate.