Geometry
HS Mathematics
Unit: 01 Lesson: 01
Points, Lines, and Planes (pp. 1 of 6) KEY
Background
Historically, much of geometry was developed as Euclidean geometry, or non-coordinate geometry. It
was named after the Greek mathematician Euclid. Euclid’s most important work was the 13 volumes
of The Elements of Geometry. He began his system of geometry with three undefined terms: point,
line, and plane. From those terms he defined other geometric vocabulary and postulates. Euclid then
proceeded to prove theorems using the definitions and postulates, much as we do today.
Geometric Vocabulary
Undefined terms – These terms can only be explained using examples and descriptions. These
undefined terms can be used to define other geometric terms and properties.
Term
Description
Naming
Point
Has no actual size,
used to represent an
object or location in
space
Named by a
capital letter
Line
Has no thickness or
width, used to
represent a continuous
set of linear points that
extend indefinitely in
both directions
Named by a
lowercase script
letter or by two
points on the line.
Plane
Has no thickness,
width, or depth, used
to represent a flat
surface that extends
indefinitely in all
directions.
Symbolic
Representation
xA
m
A
Q
Named by a
capital script letter
or by three noncollinear points in
the plane.
Ax
Bx
Cx
Plane Q
Plane ABC
1. Describe three real world situations that depict the concept of a point.
Answers will vary.
2. Describe three real world situations that characterize a line.
Answers will vary.
3. Describe three real world situations that characterize a plane.
Answers will vary.
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B
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Geometry
HS Mathematics
Unit: 01 Lesson: 01
Points, Lines, and Planes (pp. 2 of 6) KEY
Defined terms – All other terms in geometry must be definable and a definition includes a category
and then a list of critical attributes.
Example: Space – Set of all points, boundless and three-dimensional.
“Set of all points” – is the classification
“Boundless and three dimensional” – are the critical attributes that make this definition
different from other definitions.
Defined terms
space – Set of all points, boundless and three dimensional
collinear – Set of points, that all lie on the same line
(Hint: Two points are always collinear. Three points must be checked to determine if
they are collinear.)
non-collinear – Set of points, that do not all lie on the same line
coplanar – Set of points, or lines, that lie in the same plane
(Hint: Three points are always coplanar. Four points must be checked to determine if
they are coplanar.)
non-coplanar – Set of points, or lines, that do not lie in the same plane
skew lines – Two non-coplanar lines that do not intersect
parallel lines – Two coplanar lines that do not intersect
Intersections of geometric terms
Two lines intersect at a point
Two planes intersect at a line
B
A
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A
D
C
E
B
A line and a plane intersect at a point
Q
R
x
V
y
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P
Geometry
HS Mathematics
Unit: 01 Lesson: 01
Points, Lines, and Planes (pp. 3 of 6) KEY
Guided Practice
C
1. How many lines can you draw through A?
A
Infinitely many
D
2. How many lines can you
draw through B and C?
One unique line,
B
HJJG
BC
3. Draw and label D, between B and
HJJG C. How many different
ways can you name line BC, ( BC )?
HJJG HJJG HJJG HJJG HJJG HJJG
Six ( BC,CB, DB, BD, DC,CD )
4. Give three ways to name the line that connects the points.
E
F
Answers will vary.
G H
J
5. How many different lines can you draw through three non-collinear points, when taken two at a
time? Name them.
Three lines can be drawn, lines AB, AC, BC,
A
C
B
6. List all possible names for the given figures.
d
a.
R
S
T
U
RS , RT , RU , SR , ST , SU ,
TR ,TS ,TU UR , US , UT ,
line d (also all lines associated
with the given line segments)
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b.
X
B
Y
Z
Plane B, Plane XYZ, Plane XZY,
Plane YXZ, Plane YZX, Plane
ZXY, Plane ZYX
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Geometry
HS Mathematics
Unit: 01 Lesson: 01
Points, Lines, and Planes (pp. 4 of 6) KEY
A
F
B
C
E
D
7. Refer to the figure above to answer the questions.
a. Are A, B, and C collinear? Explain.
No…they are contained in at least two lines.
b. Are A, B, C, D, and E coplanar? Explain.
No…they are contained in at least two planes.
c. How many planes appear in this figure? Name them.
Five…plane F or BCD; ABC, ACD, ADE, ABE,
HJJG
HJJG
d. What is the intersection of AE and AB ?
Point A
HJJG
e. What is the intersection of AE and plane F?
Point E
f.
What is the intersection of plane F and plane AED?
Line ED
©2010, TESCCC
08/01/10