Question

Daniela examines the two triangles below and determines Triangle D A C is similar to triangle T R S.

Triangle D A C. Angle D is 57.9 degrees and angle C is 67 degrees.
Triangle T R S. Angle R is 55.1 degrees and angle S is 67 degrees.

Which best describes the accuracy of Daniela’s solution?
Accurate. The triangles are similar and the congruent angles are listed in corresponding order.
Inaccurate. In her statement, the corresponding vertices are written in the incorrect order.
Inaccurate. There is only one pair of congruent angles, so no statement can be made on the similarity of the triangles.
Inaccurate. The triangles are not similar because angle D is not congruent to angle R.

Answer 1

To determine the accuracy of Daniela's assessment that Triangle D A C is similar to triangle T R S, we first need to check the angles:

1. Triangle D A C has angles:
- Angle D = 57.9 degrees
- Angle C = 67 degrees

Since the sum of angles in any triangle is 180 degrees, we can find Angle A:
\[
Angle A = 180 - (Angle D + Angle C) = 180 - (57.9 + 67) = 180 - 124.9 = 55.1 \text{ degrees}
\]

2. Triangle T R S has angles:
- Angle R = 55.1 degrees
- Angle S = 67 degrees

Again, we find Angle T:
\[
Angle T = 180 - (Angle R + Angle S) = 180 - (55.1 + 67) = 180 - 122.1 = 57.9 \text{ degrees}
\]

Now, we can summarize the angles in both triangles:
- Triangle D A C: 57.9 degrees (Angle D), 67 degrees (Angle C), 55.1 degrees (Angle A)
- Triangle T R S: 55.1 degrees (Angle R), 67 degrees (Angle S), 57.9 degrees (Angle T)

Now let's check the correspondence:
- Angle D (57.9) corresponds to Angle T (57.9)
- Angle C (67) corresponds to Angle S (67)
- Angle A (55.1) corresponds to Angle R (55.1)

Since all the angles are equal and the vertices have been identified correctly with their corresponding angles, we can conclude that the triangles are indeed similar.

Thus, the correct assessment of Daniela’s solution is:
**Accurate. The triangles are similar and the congruent angles are listed in corresponding order.**