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. option 1 2 3 or 4
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. option 1 2 3 or 4
Answers
GPT-4o mini
To determine the relationship between Triangle MNL and Triangle FGH, we can analyze the information given about the angles.
We know:
- Triangle MNL has angles M (51 degrees) and L (36 degrees).
- Triangle FGH has angles F (51 degrees) and G (36 degrees).
Since the sum of the interior angles in a triangle is always 180 degrees, we can find the third angles:
For Triangle MNL:
- Angle N = 180 - (51 + 36) = 180 - 87 = 93 degrees.
For Triangle FGH:
- Angle H = 180 - (51 + 36) = 180 - 87 = 93 degrees.
Now we have:
- Angle M (51 degrees) is congruent to Angle F (51 degrees).
- Angle L (36 degrees) is congruent to Angle G (36 degrees).
- Angle N (93 degrees) is congruent to Angle H (93 degrees).
Since all corresponding angles of the two triangles are congruent, by the Angle-Angle (AA) similarity criterion, we can conclude that Triangle MNL is similar to Triangle FGH.
Thus, the best option that describes the relationship between these two triangles is:
**Option 3: 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.**
We know:
- Triangle MNL has angles M (51 degrees) and L (36 degrees).
- Triangle FGH has angles F (51 degrees) and G (36 degrees).
Since the sum of the interior angles in a triangle is always 180 degrees, we can find the third angles:
For Triangle MNL:
- Angle N = 180 - (51 + 36) = 180 - 87 = 93 degrees.
For Triangle FGH:
- Angle H = 180 - (51 + 36) = 180 - 87 = 93 degrees.
Now we have:
- Angle M (51 degrees) is congruent to Angle F (51 degrees).
- Angle L (36 degrees) is congruent to Angle G (36 degrees).
- Angle N (93 degrees) is congruent to Angle H (93 degrees).
Since all corresponding angles of the two triangles are congruent, by the Angle-Angle (AA) similarity criterion, we can conclude that Triangle MNL is similar to Triangle FGH.
Thus, the best option that describes the relationship between these two triangles is:
**Option 3: 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.**