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

Step - by - Step Solution

1. Analyze :

Given only , there is no information indicating that . Since dilations preserve angle measures, without prior knowledge of being , this statement is false.

2. Analyze is parallel to

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