Topic 1
TOOLS OF
GEOMETRY
1-1 Points, Lines, & Planes
Check Your Understanding
Aug 25, Tues
Topic 1: TOOLS of GEOMETRY
1-1
Points, Lines, & Planes
TEKS Objectives:
Topic 1:
TOOLS of
GEOMETRY
1-1
Points, Lines, & Planes
OBJECTIVE: Understand basic terms of geometry
and basic postulates of geometry.
Euclid (Greek mathematician)
Accepted
facts
“Father of Geometry”
GEOMETRY
Born
Mid-4th century BC
Died
Mid-3rd century BC
Residence
Alexandria, Hellenistic
Egypt
Fields
Mathematics
Known for
•Euclidean geometry
•Euclid's Elements
•Euclidean algorithm
Basic
terms
definitions
Euclidean Geometry is based
on three undefined terms:
point, line, and plane.
Topic 1:
TOOLS of
GEOMETRY
1-1
Points, Lines, & Planes
Vocabulary
Postulate or axiom is an accepted statement of fact.
A
B
Theorem is a statement proven to be true.
or
A point indicates location. It has no shape nor dimension.
It is named by any capital letter in the English alphabet.
C m
line m
A, B, & C are
collinear points.
A line is a set of all points that extend infinitely in both directions.
It is named by any lowercase script letter or any two points on the line.
Collinear points are points that lie on the same line.
Topic 1:
TOOLS of
GEOMETRY
1-1
Points, Lines, & Planes
OBJECTIVE: Understand basic terms of geometry
and basic postulates of geometry.
A plane is a flat surface that has no thickness.
It is named by a big script letter or any 3 non-collinear points on the plane.
Q
A
B
plane Q
or
Plane ABC
C
Space is the set of all points, boundless and three-dimensional.
Topic 1: TOOLS
of GEOMETRY
1-1
Points, Lines, & Planes
OBJECTIVES: 1. Understand basic terms of geometry.
2. Understand basic postulates of geometry.
Through any two points, there is exactly one line.
B
t
A
B
If two lines intersect, then they intersect in exactly one point.
C
In algebra, one way to solve a system of equations is
to graph the equations.
The solution of the system is (3, 2) ,
the point of intersection of the two lines graphed.
This illustrates Postulate 1-2.
Topic 1: TOOLS
of GEOMETRY
1-1
Points, Lines, & Planes
OBJECTIVES: 1. Understand basic terms of geometry.
2. Understand basic postulates of geometry.
If two planes intersect, then they intersect in exactly one line.
Through any three noncollinear points, there is exactly one plane.
Topic 1: TOOLS
of GEOMETRY
1-1
Points, Lines, & Planes
OBJECTIVES: 1. Understand basic terms of geometry.
2. Understand basic postulates of geometry.
In the figure at right, name three points that are collinear and
three points that are not collinear.
Z
Y
W
triangle
Name a plane in two different ways.
any three noncollinear points on the
plane
RST
URT
URS
STU
RSTU
Topic 1: TOOLS
of GEOMETRY
1-1
Points, Lines, & Planes
OBJECTIVES: 1. Understand basic terms of geometry.
2. Understand basic postulates of geometry.
Use the diagram at right. What is the intersection of
plane HGC and plane AED?
Shade the plane that contains X, Y, and Z?
X
Y
Z
Topic 1: TOOLS
of GEOMETRY
1-1
Points, Lines, & Planes
OBJECTIVES: 1. Understand basic terms of geometry.
2. Understand basic postulates of geometry.
1. Use the figure on the right.
2. List different names for plane Z.
plane HEF ,
plane EGH ,
plane EFG ,
or plane EFGH.
plane FGH ,
Topic 1: TOOLS
of GEOMETRY
1-1
Points, Lines, & Planes
OBJECTIVES: 1. Understand basic terms of geometry.
2. Understand basic postulates of geometry.
3. Name two planes that intersect in BF .
plane BFG and plane EFB
4. a. Shade plane VWX.
b. Name a point that is coplanar
with points V, W, and X.
Y
Topic 1: TOOLS
of GEOMETRY
1-1
Points, Lines, & Planes
OBJECTIVES: 1. Understand basic terms of geometry.
2. Understand basic postulates of geometry.
In summary,
The study of Euclidean geometry starts with
three undefined terms: point, line, and plane.
From these three undefined terms: point, line, and plane,
Euclid defined other geometric vocabulary and postulates.
Some geometric vocabulary: space, collinear points, non-collinear,
coplanar, non-coplanar, parallel lines, skew lines, intersecting
Euclidean geometry requires simple ideas and statements
accepted true without proof known as postulates (or axioms).
Euclidean geometry starts with four basic postulates:
#1: Through any two points, there is exactly one line.
#2: If two lines intersect, then they intersect in exactly one point.
#3: If two planes intersect, then they intersect in exactly one line.
#4: Through any three non-collinear points, there is exactly one plane.