Question

ribes 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

Based on the given information, we can definitively say that triangle M N L is similar to triangle F H G due to the AA Similarity Criterion.

Relationship between triangles M N L and F H G

Based on the information provided, triangle M N L is similar to triangle F H G. Here's why:

Angle M (51°) is congruent to angle F (51°).

Angle L (36°) is congruent to angle G (36°).

Since two pairs of corresponding angles are congruent, we can conclude that triangle M N L is similar to triangle F H G due to the Angle-Angle (AA) Similarity Criterion.

Here's why the other statements are incorrect:

Third Angle Theorem: This theorem applies only when all three angles of one triangle are congruent to the corresponding angles of another triangle. While two pairs of angles are congruent here, the third angle (angle N and angle H) remains unknown.

Unknown Side Lengths: Side lengths are not required for similarity based on the AA Similarity Criterion. As long as two pairs of corresponding angles are congruent, the triangles are similar regardless of their side lengths.

Therefore, based on the given information, we can definitively say that triangle M N L is similar to triangle F H G due to the AA Similarity Criterion.