Geometry

Question Analysis

The main focus is to use properties of dilation (angle preservation, side parallelism, collinearity of points, and nature of dilation) to determine which statement about and its dilated image is false.

Key Concept Explanation

Angle Preservation: Dilations preserve angle measures. So, corresponding angles in the original and dilated triangles are equal.

Side Parallelism: Corresponding sides of dilated figures are parallel.

Collinearity: Points on a line in the original figure remain on the corresponding line in the dilated figure.

Dilation Type: If the dilated figure is smaller than the original, it's a reduction; if larger, it's an enlargement.

Step - by - Step Solution

1. Analyze :

Since dilations preserve angle measures and , then . This statement is true.

2. Analyze is parallel to :

By the property of dilation, corresponding sides are parallel. But