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

The statement that best describes the relationship between the two triangles is:

Triangle MNL is similar to Triangle FGH because of the third angle theorem.

Here's why:

Angle M is congruent to Angle F (51 degrees) and Angle L is congruent to Angle G (36 degrees).

Since the sum of angles in a triangle is 180 degrees, the third angle in each triangle must also be congruent (180 - 51 - 36 = 93 degrees).

Therefore, Angle N is congruent to Angle H (93 degrees).

Congruency of corresponding angles is a sufficient condition for two triangles to be similar. This is known as the Angle-Angle Similarity (AA) postulate.

The other statements are incorrect because:

The statement about the third angle being unknown is irrelevant. We already know all the angles in both triangles.

Similar triangles have corresponding angles congruent, not similar. While it's true that corresponding angles in similar triangles are similar (meaning they have the same measure), the statement incorrectly implies that only similarity is insufficient to prove triangles similar.

Side lengths are not provided, so we cannot determine similarity based on the side-angle-side (SAS) or side-side-side (SSS) postulates.

Therefore, the most accurate description of the relationship between the two triangles is based on the third angle theorem and the Angle-Angle Similarity postulate.