Question
Julia examines the two triangles below and determines that Triangle F G H is similar to triangle L N M.
Triangle F G H. Angle F is 98.6 degrees and angle G is 61.1 degrees. Triangle L N M. Angle M is 18.3 degrees and angle L is 98.6 degrees.
Which best describes the accuracy of Julia’s solution?
Accurate. The triangles are similar and the congruent angles are listed in corresponding order.
Inaccurate. The triangles are not similar because the sum of the angles in each triangle is not 180º.
Inaccurate. The triangles are similar, but the triangles are named incorrectly. The vertices are listed out of corresponding order.
Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.
Triangle F G H. Angle F is 98.6 degrees and angle G is 61.1 degrees. Triangle L N M. Angle M is 18.3 degrees and angle L is 98.6 degrees.
Which best describes the accuracy of Julia’s solution?
Accurate. The triangles are similar and the congruent angles are listed in corresponding order.
Inaccurate. The triangles are not similar because the sum of the angles in each triangle is not 180º.
Inaccurate. The triangles are similar, but the triangles are named incorrectly. The vertices are listed out of corresponding order.
Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.
Answers
Answered by
GPT-4o mini
To determine the accuracy of Julia's solution, we need to analyze the angles in both triangles.
For Triangle F G H:
- Angle F = 98.6 degrees
- Angle G = 61.1 degrees
- To find Angle H, we can calculate it using the fact that the sum of the angles in a triangle is 180 degrees.
\[
\text{Angle H} = 180^\circ - (98.6^\circ + 61.1^\circ) = 180^\circ - 159.7^\circ = 20.3^\circ
\]
For Triangle L N M:
- Angle L = 98.6 degrees
- Angle M = 18.3 degrees
- To find Angle N, we can similarly calculate it as follows:
\[
\text{Angle N} = 180^\circ - (98.6^\circ + 18.3^\circ) = 180^\circ - 116.9^\circ = 63.1^\circ
\]
Now, let's summarize the angles:
**Triangle F G H:**
- Angle F = 98.6 degrees
- Angle G = 61.1 degrees
- Angle H = 20.3 degrees
**Triangle L N M:**
- Angle L = 98.6 degrees
- Angle N = 63.1 degrees
- Angle M = 18.3 degrees
Next, let's compare the angles:
- Angle F (98.6 degrees) corresponds to Angle L (98.6 degrees).
- Angle G (61.1 degrees) corresponds to Angle N (63.1 degrees), which are **not** equal.
- Angle H (20.3 degrees) corresponds to Angle M (18.3 degrees), which are also **not** equal.
Since the angles do not match up correctly, we can conclude that the triangles are **not similar**.
Therefore, the correct assessment of Julia's solution is:
**Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.**
For Triangle F G H:
- Angle F = 98.6 degrees
- Angle G = 61.1 degrees
- To find Angle H, we can calculate it using the fact that the sum of the angles in a triangle is 180 degrees.
\[
\text{Angle H} = 180^\circ - (98.6^\circ + 61.1^\circ) = 180^\circ - 159.7^\circ = 20.3^\circ
\]
For Triangle L N M:
- Angle L = 98.6 degrees
- Angle M = 18.3 degrees
- To find Angle N, we can similarly calculate it as follows:
\[
\text{Angle N} = 180^\circ - (98.6^\circ + 18.3^\circ) = 180^\circ - 116.9^\circ = 63.1^\circ
\]
Now, let's summarize the angles:
**Triangle F G H:**
- Angle F = 98.6 degrees
- Angle G = 61.1 degrees
- Angle H = 20.3 degrees
**Triangle L N M:**
- Angle L = 98.6 degrees
- Angle N = 63.1 degrees
- Angle M = 18.3 degrees
Next, let's compare the angles:
- Angle F (98.6 degrees) corresponds to Angle L (98.6 degrees).
- Angle G (61.1 degrees) corresponds to Angle N (63.1 degrees), which are **not** equal.
- Angle H (20.3 degrees) corresponds to Angle M (18.3 degrees), which are also **not** equal.
Since the angles do not match up correctly, we can conclude that the triangles are **not similar**.
Therefore, the correct assessment of Julia's solution is:
**Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.**