Question

Which best describes the relationship between the two triangles below?
Triangle M N L. Angle M is 51 degrees and angle L is 36 degrees. Triangle F H G. Angle F is 51 degrees and angle G is 36 degrees.
Triangle M L N is similar to Triangle F G H because of the third angle theorem, Angle M is congruent to angle F, Angle L is congruent to angle G, and Angle N is congruent to angle H.
Triangle M L N may or may not be similar to Triangle F G H because the third angle is unknown.
Triangle M L N is similar to Triangle F G H because of the angle-angle criterion, Angle M is similar to angle F, Angle L is similar to angle G, and Angle N is similar to angle H.
Triangle M L N may or may not be similar to Triangle F G H because the side lengths are unknown.

Answer 1

Triangle M L N is similar to Triangle F G H by the angle–angle (AA) criterion. Angle M = Angle F (51°) and Angle L = Angle G (36°), so the third angles are also equal and the triangles are similar.