Question

Drawing Conclusions about a Dilated Triangle
Consider these two triangles. Triangle A'B'C' is the dilated figure with a scale factor of 3.

Triangle A B C has side lengths 5 centimeters, 7 centimeters, 3 centimeters. Triangle A prime B prime C prime.

What can be concluded about the two triangles? Check all that apply.
The triangles are similar.
The corresponding sides are proportional.
The length of A'B' is 15.
The length of B'C' is 9.
The dilati

Answer 1

Select:
- The triangles are similar. (Yes.)
- The corresponding sides are proportional. (Yes.)
- The length of A'B' is 15. (Yes, 5 × 3 = 15.)
- The length of B'C' is 9. (No — the side of length 3 dilates to 9, but B C = 7 dilates to 21, so B'C' = 21.)

Reason: dilation by factor 3 multiplies every side by 3, so the sides 5, 7, 3 become 15, 21, 9 respectively.