Final answer:
After a dilation with a scale factor of 3, the length ca of Δabc becomes 3 times longer becoming fd in Δdef. Angles remain unchanged during dilation, making statement 2 false. Due to proportionality, statement 4 is also correct.
Step-by-step explanation:
After a dilation with a scale factor of 3 about the origin, Δabc maps onto Δdef. We must identify which statement is true regarding the transformation. Let's evaluate each statement given:
- 3 · ca = fd - This is true. The dilation with a factor of 3 will multiply all distances by 3. Therefore, if ca represents a length in Δabc, then fd, which is its corresponding length in Δdef, will be 3 times as long.
- m∠b = 3 · m∠e - This is false. Dilation affects lengths, not angle measures. Thus, angle measures remain the same in a dilation.
- Line segment ba is congruent to segment ed - This is false. Dilation with a scale factor of 3 will make ed 3 times longer than ba.
- Line segment ab over line segment de is equal to line segment bc over line segment ac. This statement is true because dilation maintains the proportionality of sides. The ratio of corresponding sides in similar triangles is constant.
Thus, the correct statements are 1 and 4.