Question

Triangle
, shown here, is dilated by a scale factor of 2 to form
.

Triangle A-B-C shows angle A 15 degrees, angle B 100 degrees, and angle C 65 degrees. The length of A-B is 22 m-m, B-C is 6 m-m, and C-A is 24 m-m.

Which statement is true?

A.
triangle A'B'C' has sides measuring 6 mm, 22 mm, and 24 mm.

B.
triangle A'B'C' has angles measuring 30°, 130°, and 200°.

C.
triangle A'B'C' has sides measuring 8 mm, 24 mm, and 26 mm.

D.
triangle A'B' C" has angles measuring 15°, 65°, and 100°.

Answer 1

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°.**