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WARM-UP
2/1/13
Describe any points, lines and planes you see in this picture
UNIT 2: INTRODUCTION
TO GEOMETRY
Essential Question:
How do the basic properties of geometry apply to the real world?
How do you use deductive reasoning, logic, and mathematical
properties to help you draw conclusions?
Bonus Question:
Write real-world examples of conditionals and converses that
meet the following criteria, and explain each answer.
A) Write a conditional that is true but whose converse is false.
B) Write a true conditional whose converse is also true.
Points, Lines, and Planes
POINT
Definition: A point is an indication of a location. A point has
no size.
A point is represented by a small dot and is named by a
capital letter
Example:
A
Name: Point A
LINE
Definition: A line is a series of points that extends in two
opposite directions without end.
You can name a line by any two points on the line. Another
way to name a line is with a single lowercase letter.
A
B
C
m
Names:
**must be only two points**
COLLINEAR POINTS
Definition: Collinear points are points that lie on the same
line.
In the picture below, points A and B are collinear but C is not
B
A
Name the collinear points:
C
PLANE
Definition: A plane is a flat surface that has no thickness. A
plane contains many lines and extends without end in the
directions of all its lines.
You can name a plane by either a single capital letter or by at
least three of its non-collinear points.
A
B
C
Vertical
Horizontal Plane
Plane
P
PLANE
Names:
D
C
B
A
N
COPLANAR
Definition: Points and lines in the same plane are coplanar.
M
D
C
B
A
P
N
NAMING A PLANE
SPACE:
Space is the boundless, three-dimensional set of all points
INTERSECTION
Intersection: the set of points that two figures have in
common.
BASIC POSTULATES
OF GEOMETRY
(A Postulate is a rule accepted as true without
proof)
Draw two points and connect the points.
What is the geometric figure.
POSTULATE 1-1
Through any two points there is exactly one line.
Line t is the only line that passes through points A and B.
B
A
t
POSTULATE 1-2
If two lines intersect, then they intersect in exactly one point
AE and BD intersect at C
A
B
C
D
E
What is the intersection of the
front wall and the ceiling?
POSTULATE 1-3
If two planes intersect, then they intersect in exactly one line.
Plane RST and plane STW intersect in ST
R
S
T
W
POSTULATE 1-4
Through any three noncollinear points there is exactly one
plane
a) Name the plane on the bottom of the box
b) Shade the plane that contains E, H, and C.
c) Name another point that is in the same plane of point A, B, and C.
d) Name another point that is coplanar with points E, H, and C.
e) Are points A and G collinear?
2. NAME THE
INTERSECTION OF…
A. Planes HGF and GCB
GF
B. Planes HDC and DAB
DC
C. Planes EHD and FGC
None
d. Plane EFB and
Point B
e. Plane HEB and
Point C
f. Plane HEF and
Point F
Line Segments, Rays, Parallel Lines and Planes
LINE SEGMENT
Definition: A segment is a part of a line
consisting of two endpoints and all points
between
Names:
AB or BA
RAY
Definition: A ray is the part of a line consisting of
one endpoint and all the points of the line on one
side of the endpoint.
OPPOSITE RAYS
Name three segments.
Name four different rays.
Name two opposite rays.
Perpendicular Lines: lines that intersect to
form right angles.
M
n
WHAT ARE PARALLEL
LINES?
Are you sure you have the correct definition?
Definition: Parallel Lines are coplanar lines that do not intersect
What other type of lines do not intersect????
SKEW LINES
Definition: Skew Lines are noncoplanar lines that do not
intersect
Are there any in the classroom?
Name the segments
parallel to:
AB
EH
DC
Name a pair of skew
lines.
PARALLEL PLANES:
Parallel Planes: planes that do not intersect.
EX. Top ll
bottom
HGFE ll DCBA
NAME A PAIR OF
PARALLEL PLANES.
HOMEWORK
1-3 Segments, Rays, Parallel Lines
and Planes Worksheet
Quiz Wednesday!