Question

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

Two line segments KL and MN intersect at P. Segments MK and LN are parallel to each other.

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

Angle KMP is congruent to angle LNP because they are vertical angles.
Angle KMP is congruent to angle LNP because they are alternate interior angles.
Angle KPM is congruent to angle LPN because alternate exterior angles are congruent.
Angle KPM is congruent to angle LPN because corresponding angles are congruent.

Answer 1

Answer:

Angle KMP is congruent to angle LNP because they are alternate interior angles.

Step-by-step explanation:

Alternate interior angles are angles inside the parallel lines and on opposite sides of the transversal.

KM and NL are parallel to one another.  KMP and LNP both fall between the parallel lines; this makes them interior.

KL is a transversal for the two parallel lines.  KMP and LNP are on opposite sides of the transversal; this makes them alternate.

Therefore they are alternate interior angles.