Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 2 - Section 2.6 - Symmetry and Transformations - Exercises - Page 111: 35

Answer

(a) There are 9 diagonals. (b) Two diagonals lie in the exterior of the hexagon.

Work Step by Step

(a) The hexagon $ABCB'A'D$ has 6 vertices. We can find the number of diagonals $D$: $D = \frac{n~(n-3)}{2} = \frac{(6)(6-3)}{2} = 9$ (b) When we draw the nine diagonals. we can see that two diagonals lie outside the hexagon. The diagonal $AA'$ and the diagonal $BB'$ lie outside the hexagon.
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