McDougal Littell Jurgensen Geometry: Student Edition Geometry
5th Edition
ISBN: 9780395977279
Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Publisher: Houghton Mifflin Company College Division
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Chapter 9.5, Problem 24WE
a.
To determine
To find:The reason thatthe numbered
a.
Expert Solution
Answer to Problem 24WE
Numbered angles are congruent because their corresponding arcs are also congruent.
Explanation of Solution
Giveninformation: A regular polygon with 7 sides is given as shown in below figure,
Concept used:Use following properties of a
(i) By theorem 9.4, congruent chords have congruent arcs.
(ii) In a circle, congruent arcs subtend congruent inscribed angles on their remaining arcs.
To prove: In given figure, all number angles are congruent.
Key steps of proof of case III:
- Circumscribe a circle along given regular polygon with 7 sides.
- Thus, congruent sides of regular polygon are congruent chords of this circle.
- By above (i) concept, their corresponding arcs are also congruent.
- Now as these congruent arcs make numbered inscribed angles, by above concept (ii), these numbered angles will also be congruent.
Conclusion: Thus,It concludes that all numbered angles are congruent as their corresponding arcs of circumscribed circle are also congruent.
b.
To determine
To find:If angles inscribed by arcs of a regular polygon are congruent, irrespective of its total sides in it.
b.
Expert Solution
Answer to Problem 24WE
In a regular polygon of any number of sides, the inscribed angles by its arcs are always congruent.
Explanation of Solution
Giveninformation: A regular polygon with 7 sides is given as shown in below figure,
Concept used:Use following properties of a circle,
(i) By theorem 9.4, congruent chords have congruent arcs.
(ii) In a circle, congruent arcs subtend congruent inscribed angles on their remaining arcs.
To prove: If result of part (a) is applicable to a regular polygon with any number of its sides.
Key steps of proof of case III:
- Circumscribe a circle along a regular polygon with any number of sides.
- Thus, congruent sides of regular polygon are congruent chords of this circle.
- By above (i) concept, their corresponding arcs are also congruent.
- Now as these congruent arcs make numbered inscribed angles, by above concept (ii), these numbered angles will also be congruent.
Conclusion: Thus, It concludes that all numbered angles are congruent as their corresponding arcs of circumscribed circle are also congruent. And it does not depend on number of sides of the regular polygon.
Chapter 9 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
Ch. 9.1 - Prob. 1CECh. 9.1 - Prob. 2CECh. 9.1 - Prob. 3CECh. 9.1 - Prob. 4CECh. 9.1 - Prob. 5CECh. 9.1 - Prob. 6CECh. 9.1 - Prob. 7CECh. 9.1 - Prob. 8CECh. 9.1 - Prob. 9CECh. 9.1 - Prob. 10CE
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Prob. 22WECh. 9.2 - Prob. 23WECh. 9.2 - Prob. 1MRECh. 9.2 - Prob. 2MRECh. 9.2 - Prob. 3MRECh. 9.3 - Prob. 1CECh. 9.3 - Prob. 2CECh. 9.3 - Prob. 3CECh. 9.3 - Prob. 4CECh. 9.3 - Prob. 5CECh. 9.3 - Prob. 6CECh. 9.3 - Prob. 7CECh. 9.3 - Prob. 8CECh. 9.3 - Prob. 9CECh. 9.3 - Prob. 10CECh. 9.3 - Prob. 11CECh. 9.3 - Prob. 12CECh. 9.3 - Prob. 13CECh. 9.3 - Prob. 1WECh. 9.3 - Prob. 2WECh. 9.3 - Prob. 3WECh. 9.3 - Prob. 4WECh. 9.3 - Prob. 5WECh. 9.3 - Prob. 6WECh. 9.3 - Prob. 7WECh. 9.3 - Prob. 8WECh. 9.3 - Prob. 9WECh. 9.3 - Prob. 10WECh. 9.3 - Prob. 11WECh. 9.3 - Prob. 12WECh. 9.3 - Prob. 13WECh. 9.3 - Prob. 14WECh. 9.3 - Prob. 15WECh. 9.3 - Prob. 16WECh. 9.3 - Prob. 17WECh. 9.3 - Prob. 18WECh. 9.3 - Prob. 19WECh. 9.3 - Prob. 20WECh. 9.3 - Prob. 21WECh. 9.3 - Prob. 22WECh. 9.3 - Prob. 23WECh. 9.3 - Prob. 24WECh. 9.4 - Prob. 1CECh. 9.4 - Prob. 2CECh. 9.4 - Prob. 3CECh. 9.4 - Prob. 4CECh. 9.4 - Prob. 5CECh. 9.4 - Prob. 6CECh. 9.4 - Prob. 7CECh. 9.4 - Prob. 1WECh. 9.4 - Prob. 2WECh. 9.4 - Prob. 3WECh. 9.4 - 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