Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Transcribed Image Text:**Title: Understanding Transformations in Geometry**
**Introduction**
In geometry, transformations refer to the movement of figures in a plane. Common transformations include translations, rotations, reflections, and dilations. A rigid transformation (isometry) preserves the size and shape of a figure, meaning the figure's properties remain unchanged. Let's examine four examples of triangular transformations and identify which does not represent a rigid transformation.
**Description of the Transformation Examples**
1. **Image A**:
- This shows a blue triangle labeled as \( \triangle ABC \) and an overlapping green triangle labeled as \( \triangle A'B'C' \).
- The transformation does not change the triangle’s size, indicating a rigid transformation, likely a rotation or reflection.
2. **Image B**:
- Here, a blue triangle \( \triangle ABC \) is shown alongside a green triangle \( \triangle A'B'C' \) that appears non-overlapping, and the green triangle is oriented differently.
- The size remains the same, which suggests a rigid transformation, likely a rotation or translation.
3. **Image C**:
- A blue triangle \( \triangle ABC \) and a green triangle \( \triangle A'B'C' \) are given, and both overlap.
- One is a reflection or translation where the size is preserved, indicating a rigid transformation.
4. **Image D**:
- A blue triangle \( \triangle ABC \) and a noticeably smaller green triangle \( \triangle A'B'C' \) are displayed.
- The green triangle is a scaled-down version of the blue triangle, which indicates a dilation, a non-rigid transformation as the size is not preserved.
**Conclusion**
Among the transformations displayed, Image D is the only one that does not represent a rigid transformation due to the change in size (dilation) of the triangle. Understanding and identifying the type of transformation helps in preserving the properties of geometric figures.
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