10) Nhich of the following statements are true about the regular polygon? Select all that apply. It is a nonagon. All of the triangles created are right triangles. Angle GFE is 140° Angle AJB is 40° It is a decagon All of the triangles created are isosceles.
10) Nhich of the following statements are true about the regular polygon? Select all that apply. It is a nonagon. All of the triangles created are right triangles. Angle GFE is 140° Angle AJB is 40° It is a decagon All of the triangles created are isosceles.
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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![**Question 10)**
An illustration of a regular polygon is provided. The polygon has 10 vertices labeled A, B, C, D, E, F, G, H, I, and J. Lines are drawn from the center of the polygon to each vertex, creating multiple triangles. Each side of the triangle is a side of the polygon or a radius of the circumscribed circle.
**Question:**
Which of the following statements are true about the regular polygon? Select all that apply.
- [ ] It is a nonagon.
- [ ] All of the triangles created are right triangles.
- [ ] Angle GFE is **140°**
- [ ] Angle AJB is **40°**
- [ ] It is a decagon.
- [ ] All of the triangles created are isosceles.
**Explanation of the Diagram:**
The diagram shows a regular decagon (a polygon with 10 equal sides) inscribed in a circle. Each vertex of the decagon is connected to the center of the circle, forming 10 isosceles triangles (since two sides are radii of the circle and thus equal).
**Correct Answers:**
- The statement "It is a decagon" is true.
- The statement "All of the triangles created are isosceles" is true, as each triangle has two equal sides (the radii of the circle).
Other statements are not true for the following reasons:
- It is not a nonagon, as a nonagon has 9 sides.
- Not all of the triangles created are right triangles (a right triangle has one 90° angle, which is not the case here).
- Angle GFE and Angle AJB are not specified in the problem, but typical interior angles of a decagon and other calculations can clarify their incorrectness based on geometric rules.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad4489ae-192a-4145-a2b1-a7dea3a6e6b1%2F111f6a4f-8820-4a09-8808-8964771e4a10%2Fg9dv5jh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 10)**
An illustration of a regular polygon is provided. The polygon has 10 vertices labeled A, B, C, D, E, F, G, H, I, and J. Lines are drawn from the center of the polygon to each vertex, creating multiple triangles. Each side of the triangle is a side of the polygon or a radius of the circumscribed circle.
**Question:**
Which of the following statements are true about the regular polygon? Select all that apply.
- [ ] It is a nonagon.
- [ ] All of the triangles created are right triangles.
- [ ] Angle GFE is **140°**
- [ ] Angle AJB is **40°**
- [ ] It is a decagon.
- [ ] All of the triangles created are isosceles.
**Explanation of the Diagram:**
The diagram shows a regular decagon (a polygon with 10 equal sides) inscribed in a circle. Each vertex of the decagon is connected to the center of the circle, forming 10 isosceles triangles (since two sides are radii of the circle and thus equal).
**Correct Answers:**
- The statement "It is a decagon" is true.
- The statement "All of the triangles created are isosceles" is true, as each triangle has two equal sides (the radii of the circle).
Other statements are not true for the following reasons:
- It is not a nonagon, as a nonagon has 9 sides.
- Not all of the triangles created are right triangles (a right triangle has one 90° angle, which is not the case here).
- Angle GFE and Angle AJB are not specified in the problem, but typical interior angles of a decagon and other calculations can clarify their incorrectness based on geometric rules.
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