Name
LESSON
1-1
Date
Class
Challenge
Exploring Relationships
Use the figure of the kite for Exercises 1–4.
#
1. Name three collinear points that lie in plane P.
!
X, A, C
8
2. Name a point that is coplanar with Y and F.
$
"
Sample answer: E
9
_
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3. Name two planes that intersect CD .
&
P and R
‹__› ‹___›
‹__›
4. Write True or False: AE, CG, and FJ intersect. If true, then name the intersection.
If false, then explain why the lines do not intersect.
*
True; the lines intersect at point J.
Lines in a plane divide the plane into regions. The number of regions depends on the
relationship between the lines. Consider two lines in a plane.
1
2
3
If the lines are
parallel, three
regions are
determined.
5. a. Complete the table.
b. Describe the pattern in
the table.
Sample answer:
The pattern is one of
increasing differences.
1
3
4
Number of lines
in a plane
0
1
2
3
4
Greatest number of
regions determined
1
2
4
7
11
c. Predict the greatest number of regions determined
by five lines in a plane.
16 regions (16 2 11 5 5)
Answer:
5d. Drawings will vary.
6. You can use an approach similar to the one in Exercise 5
to investigate the greatest possible number of points of
intersection for n lines in a plane. Make a table and look
for a pattern. What is the greatest possible number of
points of intersection for six lines in a plane?
8
d. On a separate sheet of paper, make a drawing to verify
your prediction from part c.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
If the lines
intersect, four
regions are
determined.
2
15
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