Geometry

Question Analysis

The main focus is to use 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: Dilations preserve angle measures. So, corresponding angles in the original and dilated quadrilaterals are equal.

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 larger than the original, it's an enlargement; if smaller, it's 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. So

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