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You are given a box of matches. The matches are all the same length and you are not allowed to break any. With these matchsticks, you find that you can form all six possible pairs of the four regular figures: triangle, square, pentagon, and hexagon, using all the matches every time. For example, for a box containing 11 matches you can form the three pairs of figures as shown above but it is not possible to form the other three pairs: triangle and hexagon; square and pentagon; nor square and hexagon. Hence the box you are given cannot contain 11 matches. What is the minimum possible number of matches you can have in the box so that you can make all possible pairs of the given shapes using all the matchsticks in each pair? What other numbers of matches will work? Provide reasons why these other numbers work. Consider some other shapes with different number of sides. IS there a general rule to relate the number of matchsticks to make all the pairs and the number of sides in the shapes.

You are given a box of matches. The matches are all the same length and you are not allowed to break any. With these matchsticks, you find that you can form all six possible pairs of the four regular figures: triangle, square, pentagon, and hexagon, using all the matches every time. For example, for a box containing 11 matches you can form the three pairs of figures as shown above but it is not possible to form the other three pairs: triangle and hexagon; square and pentagon; nor square and hexagon. Hence the box you are given cannot contain 11 matches. What is the minimum possible number of matches you can have in the box so that you can make all possible pairs of the given shapes using all the matchsticks in each pair? What other numbers of matches will work? Provide reasons why these other numbers work. Consider some other shapes with different number of sides. IS there a general rule to relate the number of matchsticks to make all the pairs and the number of sides in the shapes.

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.
Chapter2: Parallel Lines
Section2.5: Convex Polygons
Problem 41E
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I need a process, and this formula can be applied to any shape with different number of sides. Thank you so much!

9. A regular problem A You are given a box of matches. The matches are all the same length and you are not allowed to break any. With these matchsticks, you find that you can form all six possible pairs of the four regular figures: triangle, square, pentagon, and hexagon, using all the matches every time. For example, for a box containing 11 matches you can form the three pairs of figures as shown above but it is not possible to form the other three pairs: triangle and hexagon; square and pentagon; nor square and hexagon. Hence the box you are given cannot contain 11 matches. What is the minimum possible number of matches you can have in the box so that you can make all possible pairs of the given shapes using all the matchsticks in each pair? What other numbers of matches will work? Provide reasons why these other numbers work. Consider some other shapes with different number of sides. IS there a general rule to relate the number of matchsticks to make all the pairs and the number of sides in the shapes.
Transcribed Image Text:9. A regular problem A You are given a box of matches. The matches are all the same length and you are not allowed to break any. With these matchsticks, you find that you can form all six possible pairs of the four regular figures: triangle, square, pentagon, and hexagon, using all the matches every time. For example, for a box containing 11 matches you can form the three pairs of figures as shown above but it is not possible to form the other three pairs: triangle and hexagon; square and pentagon; nor square and hexagon. Hence the box you are given cannot contain 11 matches. What is the minimum possible number of matches you can have in the box so that you can make all possible pairs of the given shapes using all the matchsticks in each pair? What other numbers of matches will work? Provide reasons why these other numbers work. Consider some other shapes with different number of sides. IS there a general rule to relate the number of matchsticks to make all the pairs and the number of sides in the shapes.
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