To determine the similarity statement for ΔPQR and ΔXYZ, we need to check the angles.
Given:
-
For ΔPQR:
- m∠P = 28°
- m∠Q = 115°
-
For ΔXYZ:
- m∠X = 28°
- m∠Z = 115°
To find m∠Y in ΔPQR, we can use the fact that the sum of angles in a triangle is 180°:
m∠R = 180° - m∠P - m∠Q m∠R = 180° - 28° - 115° = 37°
Now, since we have:
- m∠P = m∠X = 28°
- m∠Q (not given for ΔXYZ) is not relevant since we need to check the angles that are given.
Next, for ΔXYZ, since we have:
- m∠Z = 115°
- We can find m∠Y the same way: m∠Y = 180° - m∠X - m∠Z m∠Y = 180° - 28° - 115° = 37°
Now we have:
- m∠P = m∠X = 28°
- m∠R = m∠Y = 37°
- m∠Q = m∠Z = 115°
Since the angles are all equal (28°, 115°, and 37° in both triangles), we can conclude that:
ΔPQR ∼ ΔXYZ.
The correct similarity statement is therefore: ΔPQR ∼ ΔXYZ.