Geometry

Question Analysis

This question is about understanding the properties of dilation in geometry. We must use the rules of angle preservation, side parallelism, collinearity of points, and the nature of dilation (enlargement or reduction) to determine which statement is false.

Key Concept Explanation

Angle Preservation: Dilation is a transformation that keeps angle measures the same. So, corresponding angles in the original and dilated triangles are equal.

Side Parallelism: Corresponding sides of the original and dilated triangles are parallel.

Collinearity: Points that are on the same 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. For :

Since dilation preserves angles, and we know , then . This statement is true.

2. For is parallel to :

By the property of dilation, corresponding sides are parallel. So and being corresponding sides means . This statement is true.

3. For is not on the line :

In dilation, corresponding points (including

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