Geo_Book_Answers

Answers to Exercises
1.
See table below.
2. n 1, 36
LESSON 2.3
3. You can draw a diagonal from one vertex to all
the other vertices except three: the two adjacent
vertices and the vertex itself.
4. n(n 3)
,
2
560
5. n(n 1)
,595
2
6. n(n 1)
,595
2
7. Answers will include relationships between
points in Exercises 5 and 6 and vertices of a polygon.
The total number of segments connecting n random
points is the number of diagonals of the n-sided
polygon, n(n 3)
, 2 plus the number of sides, n.
Thus, the total number of segments connecting n
random points is n(n 3) 2n
n(n 3) 2n
2 2
n2 3n
2n n
2
2 n
2 n(n 1)
. 2
1. (Lesson 2.3)
26 ANSWERS TO EXERCISES
2
8. Use n(n 1)
2
to get 780 direct lines. Use a central
hub with a line to each house to get 40 lines. The
art shows the direct-line solution and the practical
solution for six houses.
9. Use points for the 10 teams and segments
connecting them to represent four games played
between them. So, use 4 n(n 1)
2 to get 180 games
played.
10. If n(n
1)
2 66, then n(n 1) 132. What
two consecutive numbers multiply to equal 132?
12 times 11. Thus, there were 12 people at the
party.
11. true
12. true
13. False; an isosceles right triangle has two sides
congruent.
14. false
A
E
B C
D
AED and BED are
not a linear pair.
15. False; they are parallel.
16. true
17. False; a rectangle is a parallelogram with all of
its angles congruent.
18. False; a diagonal is a segment in a polygon
connecting any two nonconsecutive vertices.
19. true
20. 5049
Lines 1 2 3 4 5 … n … 35
Regions 2 4 6 8 10 … 2n … 70