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.
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.
Answers
GPT-4o mini
To determine the relationship between Triangle MNL and Triangle FGH, we can analyze the angles provided.
In Triangle MNL:
- Angle M = 51 degrees
- Angle L = 36 degrees
- By the triangle sum theorem, the sum of the angles in a triangle is always 180 degrees, so Angle N can be calculated as:
\[
Angle N = 180 - Angle M - Angle L = 180 - 51 - 36 = 93 \text{ degrees}
\]
In Triangle FGH:
- Angle F = 51 degrees
- Angle G = 36 degrees
- Similarly, we can find Angle H:
\[
Angle H = 180 - Angle F - Angle G = 180 - 51 - 36 = 93 \text{ degrees}
\]
Both triangles have the following angles:
- Angle M ≅ Angle F = 51 degrees
- Angle L ≅ Angle G = 36 degrees
- Angle N ≅ Angle H = 93 degrees
Since all corresponding angles of the two triangles are equal, Triangle MNL is similar to Triangle FGH by the Angle-Angle (AA) criterion.
Thus, the best description of the relationship between the two triangles is:
**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.**
In Triangle MNL:
- Angle M = 51 degrees
- Angle L = 36 degrees
- By the triangle sum theorem, the sum of the angles in a triangle is always 180 degrees, so Angle N can be calculated as:
\[
Angle N = 180 - Angle M - Angle L = 180 - 51 - 36 = 93 \text{ degrees}
\]
In Triangle FGH:
- Angle F = 51 degrees
- Angle G = 36 degrees
- Similarly, we can find Angle H:
\[
Angle H = 180 - Angle F - Angle G = 180 - 51 - 36 = 93 \text{ degrees}
\]
Both triangles have the following angles:
- Angle M ≅ Angle F = 51 degrees
- Angle L ≅ Angle G = 36 degrees
- Angle N ≅ Angle H = 93 degrees
Since all corresponding angles of the two triangles are equal, Triangle MNL is similar to Triangle FGH by the Angle-Angle (AA) criterion.
Thus, the best description of the relationship between the two triangles is:
**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.**