Geometry

Question Analysis

The main focus is to apply the properties of dilation (angle preservation, side parallelism, collinearity of points, and nature of dilation) to identify the false statement regarding and its dilated image .

Key Concept Explanation

Angle Preservation: In dilation, corresponding angles in the original and dilated figures are congruent.

Side Parallelism: Corresponding sides of dilated figures are parallel.

Collinearity: Points that are not on a line in the original figure will not be on the corresponding line in the dilated figure in an incorrect way.

Dilation Type: If the dilated figure is smaller than the original, it is a reduction; if larger, 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. So