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Here are four triangles that have undergone a different transformation. Which image does not show a rigid transformation? A B

Here are four triangles that have undergone a different transformation. Which image does not show a rigid transformation? A B

Elementary Geometry For College Students, 7e
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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**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.
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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