Question

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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 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.

Explanation:

Triangles are similar if all of the angles are congruent and corresponding to the other triangle and the sides are proportionate. It is important to note that if the angles are congruent then the sides must be proportionate; so, the side lengths are not necessary. Additionally, the third angle theorem states that if two known angles are congruent then the third angles must also be congruent. So, the two triangles must be similar because all of the angles are congruent to their corresponding angles.