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 determine which statement about quadrilateral  and its dilated image  is false.

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 on a line in the original figure remain on the corresponding line in the dilated figure.

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

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.

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