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Enrique stated that the figures below were regular polygons because the sides in each figure are equal. How would you respond to Enrique? ★

Enrique stated that the figures below were regular polygons because the sides in each figure are equal. How would you respond to Enrique? ★

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter12: Angle Relationships And Transformations
Section12.5: Reflections And Symmetry
Problem 20E
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### Understanding Regular Polygons **Prompt:** Enrique stated that the figures below were regular polygons because the sides in each figure are equal. How would you respond to Enrique? **Explanation:** In the image, there are two figures displayed side by side: 1. The first figure on the left is an arrow-like shape, which appears to have unequal sides. 2. The second figure on the right is a star shape. This star has equal-length sides with vertices marked by orange dots. **Response to Enrique:** To understand whether these shapes are regular polygons, let's first define what a regular polygon is. A regular polygon is a geometric figure with all sides of equal length and all interior angles equal. - **First Figure (Arrow-like shape):** This does not appear to be a regular polygon because its sides do not have equal lengths and its angles are not equal either. - **Second Figure (Star shape):** While the sides of the star might be equal, for it to be considered a regular polygon, its angles must also be equal. Since the interior angles of this star's points are not the same as the angles where the points meet the inner pentagon, it disqualifies the star from being a regular polygon. Therefore, both figures provided in the image are not regular polygons. Regular polygons must have both equal side lengths and equal interior angles, which these figures do not satisfy.
Transcribed Image Text:### Understanding Regular Polygons **Prompt:** Enrique stated that the figures below were regular polygons because the sides in each figure are equal. How would you respond to Enrique? **Explanation:** In the image, there are two figures displayed side by side: 1. The first figure on the left is an arrow-like shape, which appears to have unequal sides. 2. The second figure on the right is a star shape. This star has equal-length sides with vertices marked by orange dots. **Response to Enrique:** To understand whether these shapes are regular polygons, let's first define what a regular polygon is. A regular polygon is a geometric figure with all sides of equal length and all interior angles equal. - **First Figure (Arrow-like shape):** This does not appear to be a regular polygon because its sides do not have equal lengths and its angles are not equal either. - **Second Figure (Star shape):** While the sides of the star might be equal, for it to be considered a regular polygon, its angles must also be equal. Since the interior angles of this star's points are not the same as the angles where the points meet the inner pentagon, it disqualifies the star from being a regular polygon. Therefore, both figures provided in the image are not regular polygons. Regular polygons must have both equal side lengths and equal interior angles, which these figures do not satisfy.
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