Question

A figure containing angle CDE is dilated by a scale factor of 1/3 to form a new figure which contains angle CDE prime. CDE prime measures 40 degrees. what is the measure of CDE?​

Answer 1

Angle measures remain constant in a dilation, so if angle CDE prime is 40 degrees after dilation, the original angle CDE is also 40 degrees.

Step-by-step explanation:

The student is asking about the properties of dilation in geometry, specifically the angle measure after a dilation process with a given scale factor.

A dilation is a proportional change in the size of a shape. The length of each side in the shape is multiplied by the same number, but the shape and its angle measures remain the same.

The following properties are preserved between the pre-image and its image when dilating:

1. Angle measure (angles stay the same)
2. Parallelism (things that were parallel are still parallel)
3. Collinearity (points on a line, remain on the line).

When a geometric figure is dilated, the angles remain the same; only the lengths of the sides are altered by the scale factor.

Therefore, if the angle CDE prime is 40 degrees after a dilation by a scale factor of 1/3, the measure of the original angle CDE is also 40 degrees, because angle measures are preserved under dilation.