To analyze the statements based on the dilation of triangle A-B-C to triangle A'-B'-C', we need to consider how dilation affects the side lengths and angles of the triangle.
Given:
- Angles: A = 15°, B = 100°, C = 65°
- Sides: A-B = 22 mm, B-C = 6 mm, C-A = 24 mm
When a triangle is dilated by a scale factor of 2:
- The angles remain unchanged.
- The side lengths are multiplied by the scale factor (in this case, 2).
Calculating the sides of triangle A'-B'-C':
- A'-B' = 22 mm * 2 = 44 mm
- B'-C' = 6 mm * 2 = 12 mm
- C'-A' = 24 mm * 2 = 48 mm
Now let's evaluate each statement:
A. Triangle A'B'C' has sides measuring 6 mm, 22 mm, and 24 mm.
- This is incorrect. The sides should measure 44 mm, 12 mm, and 48 mm.
B. Triangle A'B'C' has angles measuring 30°, 130°, and 200°.
- This is incorrect. The angles remain the same as those in triangle A-B-C: 15°, 100°, and 65°.
C. Triangle A'B'C' has sides measuring 8 mm, 24 mm, and 26 mm.
- This is incorrect. The sides should measure 44 mm, 12 mm, and 48 mm.
D. Triangle A'B'C' has angles measuring 15°, 65°, and 100°.
- This is correct. The angles remain unchanged after dilation.
Thus, the true statement is:
D. Triangle A'B'C' has angles measuring 15°, 65°, and 100°.