Question

aniela 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

Accurate. The triangles are similar and the congruent angles are listed in corresponding order.

Justification: In ΔDAC, angle A = 180 − (57.9 + 67) = 55.1°. In ΔTRS, angle T = 180 − (55.1 + 67) = 57.9°. So the angles match as D↔T (57.9°), A↔R (55.1°), C↔S (67°), so the vertex order DA C ~ TR S is correct.