1-2
Points, Lines, and Planes
PART 2
Vocabulary
Review
a
Use the diagram at the right. Complete each statement with the correct
word from the list below.
intersect
intersecting
P
b
intersection
1. Line a and line b 9 at point P.
2. The 9 of lines a and b is point P.
3. The diagram shows two 9 lines.
Vocabulary Builder
plane P
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plane (noun) playn
A
Related Word: coplanar
P
C
B
Definition: A plane is represented by a flat surface that
extends without end.
Word Origin: The word plane comes from the Latin planos, which means “flat.”
Math Usage: A plane contains infinitely many points. You can name a plane by
one capital letter or by at least three noncollinear points in the plane.
Use Your Vocabulary
Write T for true or F for false.
4. A plane has length, width, and height.
5. A plane extends without end.
6. All points in a line are coplanar.
7. All points in a plane are collinear.
13
Lesson 1-2, Part 2
Postulates 1–1, 1–2, 1–3, and 1–4
8. Complete each postulate with line, plane, or point.
Postulate 1-1 Through any two points there is exactly one 9.
Postulate 1-2 If two distinct lines intersect, then they intersect in exactly one 9.
Postulate 1-3 If two distinct planes intersect, then they intersect in exactly one 9.
Postulate 1-4 Through any three noncollinear points there is exactly one 9.
Write P if the statement describes a postulate or U if it describes an undefined term.
9. A point indicates a location and has no size.
10. Through any two points there is exactly one line.
11. If two distinct planes intersect, then they intersect in exactly one line.
12. If two distinct lines intersect, then they intersect in exactly one point.
D
Got It? Each surface of the box at the right represents
* ) part of a plane.
A
What are the names of two planes that intersect in BF ?
* )
E
13. Circle the points that are on BF or in one of the two planes.
A
B
C
D
E
F
H
G
C
B
G
F
H
14. Circle another name for plane BFG. Underline another name for plane BFE.
ABF
BCD
BCG
CDH
* )
FGH
15. Now name two planes that intersect in BF .
B
Use the diagram at the right for Exercises 16–19.
16. The intersection of plane DFC and plane ACB is
.
17. The intersection of plane CBF and plane ACF is
.
18. The intersection of plane DFE and plane BEF is
.
19. Name two planes that do NOT intersect.
Chapter 1
C
A
14
E
F
D
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Problem 3 Finding the Intersection of Two Planes
Problem 4 Using Postulate 1–4
Got It? What plane contains points L, M, and N? Shade the plane.
M
J
20. Use the figure below. Draw LM , LN , and MN as dashed segments.
Then shade plane LMN.
M
L
J
L
K
R
N
Q
P
K
R
Q
P
N
Underline the correct word to complete the sentence.
21. LM , LN , and MN form a triangle / rectangle .
22. Name the plane.
_______________________________________________________________________
Lesson Check • Do you UNDERSTAND?
Reasoning Can two planes intersect at a ray or a segment? Explain.
23. Complete Postulate 1-3.
If two distinct planes intersect, then they intersect in exactly one 9.
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
24. Circle the figures that extend without end.
line
plane
ray
segment
25. Now answer the question.
_______________________________________________________________________
_______________________________________________________________________
Math Success
Check off the vocabulary words that you understand.
point
line
plane
segment
ray
postulate
axiom
Rate how well you understand points, lines, and planes.
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Lesson 1-2, Part 2