Question

Which statements about the relationship between the two triangles below are true? Check all that apply.

Triangle A C D. Angle D is 60 degrees and angle A is 74.9 degrees. Triangle R S T. Angle R is 74.9 degrees and angle S is 45.1 degrees.
Angle C is congruent to angle T
Angle C is congruent to angle S
Angle D is congruent to angle T
Triangle D C A is congruent to triangle T S R
Triangle D C A is similar to triangle T S R
Triangle C A D is similar to triangle T R S
Triangle C A D is congruent to triangle T R S

Answer 1

Compute the missing angles: in triangle A C D, C = 180 − 60 − 74.9 = 45.1°. In triangle R S T, T = 180 − 74.9 − 45.1 = 60°.

So the angle matches are A ↔ R (74.9°), C ↔ S (45.1°), D ↔ T (60°).

True statements:
- Angle C is congruent to angle S
- Angle D is congruent to angle T
- Triangle D C A is similar to triangle T S R

False statements:
- Angle C is congruent to angle T
- Triangle D C A is congruent to triangle T S R (AAA gives similarity, not congruence)
- Triangle C A D is similar to triangle T R S (order does not match)
- Triangle C A D is congruent to triangle T R S