Question

Select the similarity statement for ΔPQR
(with m∠P=28°
, m∠Q=115°
) ΔXYZ
( m∠X=28°
, m∠Z=115°
).
Responses

ΔPQR∼ΔXZY

ΔPQR∼ΔXZY
- no response given

ΔPQR=ΔXZY

ΔPQR=ΔXZY
- incorrect

ΔPQR∼ΔXYZ

ΔPQR∼ΔXYZ
- no response given

ΔPQR=ΔXYZ

Answer 1

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**.