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Every quadrilateral can be inscribed in a circle. O True 23 24 25 26 27 29 False 29 30

Every quadrilateral can be inscribed in a circle. O True 23 24 25 26 27 29 False 29 30

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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Every quadrilateral can be inscribed in a circle. True/ False
**Question:** Every quadrilateral can be inscribed in a circle. - ( ) True - (•) False **Explanation:** In a cyclic quadrilateral (a quadrilateral that can be inscribed in a circle), the opposite angles must add up to 180 degrees. However, not all quadrilaterals have this property. Only those that satisfy this condition can be inscribed in a circle. For further understanding, consider the following types of quadrilaterals: 1. **Square** - Can be inscribed in a circle. 2. **Rectangle** - Can be inscribed in a circle. 3. **Rhombus** - Cannot always be inscribed in a circle unless it is also a square. 4. **Parallelogram** - Cannot always be inscribed in a circle unless it is a rectangle or square. 5. **Trapezium** - Only certain trapeziums, such as isosceles trapeziums, might be inscribed in a circle. Thus, the answer is **False** because not all quadrilaterals meet the criteria to be inscribed in a circle.
Transcribed Image Text:**Question:** Every quadrilateral can be inscribed in a circle. - ( ) True - (•) False **Explanation:** In a cyclic quadrilateral (a quadrilateral that can be inscribed in a circle), the opposite angles must add up to 180 degrees. However, not all quadrilaterals have this property. Only those that satisfy this condition can be inscribed in a circle. For further understanding, consider the following types of quadrilaterals: 1. **Square** - Can be inscribed in a circle. 2. **Rectangle** - Can be inscribed in a circle. 3. **Rhombus** - Cannot always be inscribed in a circle unless it is also a square. 4. **Parallelogram** - Cannot always be inscribed in a circle unless it is a rectangle or square. 5. **Trapezium** - Only certain trapeziums, such as isosceles trapeziums, might be inscribed in a circle. Thus, the answer is **False** because not all quadrilaterals meet the criteria to be inscribed in a circle.
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