The triangles below are similar.

Question

Triangle S R P. Angle S is 54 degrees, R is 41 degrees, P is 85 degrees. Triangle X Y Z. Angle X is 54 degrees, Z is 41 degrees, and Y is 85 degrees.

Which similarity statements describe the relationship between the two triangles? Check all that apply.
Triangle P R S is similar to triangle X Y Z
Triangle R S P is similar to triangle Z X Y
Triangle S R P is similar to triangle X Z Y
Triangle P S R is similar to Triangle Z Y X
Triangle R P S is similar to triangle Z Y X
Triangle S P R is similar to triangle X Z Y

Answer 1

To determine the similarity of the triangles, we can use the corresponding angles of the triangles S R P and X Y Z. Since the angles in both triangles are the same, we can establish the following similarity statements:

1. Triangle P R S is similar to triangle X Y Z: This statement is true because the angles match: P (85°) corresponds to Y (85°), R (41°) corresponds to Z (41°), and S (54°) corresponds to X (54°).

2. Triangle R S P is similar to triangle Z X Y: This statement is true because the angles match in the same order: R (41°) corresponds to Z (41°), S (54°) corresponds to X (54°), and P (85°) corresponds to Y (85°).

3. Triangle S R P is similar to triangle X Z Y: This statement is false because the corresponding angles do not match in that order. Z (41°) would need to correspond to R (41°), but in this similarity statement, it claims Z corresponds to S (54°).

4. Triangle P S R is similar to Triangle Z Y X: This statement is false because the angles do not correspond correctly.

5. Triangle R P S is similar to triangle Z Y X: This statement is false; the angle correspondence does not match.

6. Triangle S P R is similar to triangle X Z Y: This statement is false; the angle correspondence does not match.

In summary, the following similarity statements are correct:

• Triangle P R S is similar to triangle X Y Z
• Triangle R S P is similar to triangle Z X Y