Which of the following figures are convex and which are concave? Why? (a) O concave --- (c) convex (b) (a) Is figure (a) convex or concave? Choose the correct answer below. (d)

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 Convex and Concave Figures**

**Objective:**  
Learn to identify convex and concave figures and understand the differences between them.

**Question:**  
Which of the following figures are convex and which are concave? Why?

**Illustrations:**

- **Figure (a):** A shape resembling a triangle with curved sides.
- **Figure (b):** A shape with two symmetrical inward curves.
- **Figure (c):** A shape with an inward curve resembling a crescent.
- **Figure (d):** A shape with sharp angles creating a non-standard polygon.

**Activity:**  
(a) Is figure (a) convex or concave? Choose the correct answer below.

- ○ concave
- ○ convex

**Concept Explanation:**

A **convex** shape is one where a line segment joining any two points within the shape lies entirely inside it. A **concave** shape has at least one line segment joining two points within the shape that passes outside of it.

**Interactive Exercise:**  

- Review each figure and use the definitions provided to determine if each one is convex or concave.
- Engage with the interactive question to test your understanding.

**Additional Resources:**

- Explore more examples and practice problems to reinforce your understanding.
- Click "Get more help" for further assistance or to connect with a tutor.
Transcribed Image Text:**Title: Understanding Convex and Concave Figures** **Objective:** Learn to identify convex and concave figures and understand the differences between them. **Question:** Which of the following figures are convex and which are concave? Why? **Illustrations:** - **Figure (a):** A shape resembling a triangle with curved sides. - **Figure (b):** A shape with two symmetrical inward curves. - **Figure (c):** A shape with an inward curve resembling a crescent. - **Figure (d):** A shape with sharp angles creating a non-standard polygon. **Activity:** (a) Is figure (a) convex or concave? Choose the correct answer below. - ○ concave - ○ convex **Concept Explanation:** A **convex** shape is one where a line segment joining any two points within the shape lies entirely inside it. A **concave** shape has at least one line segment joining two points within the shape that passes outside of it. **Interactive Exercise:** - Review each figure and use the definitions provided to determine if each one is convex or concave. - Engage with the interactive question to test your understanding. **Additional Resources:** - Explore more examples and practice problems to reinforce your understanding. - Click "Get more help" for further assistance or to connect with a tutor.
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