CH 1-2
Points Lines and Planes
Warm Up
On a number line, graph each inequality.
1. x ≥ 3
-2
0
2
4
2. 2 ≤ x ≤ 6
0
2
4
6
3. x < 1 OR x > 0
0
1
P15 # 1Geometry
CH 1-2
Points Lines and Planes
Warm Up
In a sequence of starts and stops,
an elevator travels from the first
floor to the fifth floor and then to
the second floor. From there, the
elevator travels to the fourth floor
and then to the third floor. If the
floors are 3 m apart, how far has
the elevator traveled?
Geometry
CH 1-2
Points Lines and Planes
Warm Up
What is the area of the shaded figure?
Geometry
CH 1-2
Points Lines and Planes
Objectives
Define Geometry
Identify, name, and draw points, lines,
segments, rays, and planes.
Apply basic facts about points, lines,
and planes.
Geometry
CH 1-2
Points Lines and Planes
Vocabulary
undefined term
line
collinear
segment
ray
postulate
point
plane
coplanar
endpoint
opposite rays
Geometry
CH 1-2
Points Lines and Planes
Geometry (Greek) "measurement of earth or land"
The study of geometry can be broken into two broad types:
plane geometry
and
Solid geometry
Geometry
CH 1-2
Points Lines and Planes
plane geometry: which deals with only two dimensions, it
deals with objects that are flat, such as triangles and lines,
that can be drawn on a flat piece of paper.
Solid geometry: allows width, depth and height. The
world around us is obviously three-dimensional, such as
cubes and spheres.
Geometry
CH 1-2
Points Lines and Planes
The most basic figures in geometry are
undefined terms, which cannot be
defined by using other figures. The
undefined terms are: Point, Line, and
Plane which are the building blocks of
geometry.
Geometry
CH 1-2
Points Lines and Planes
Point: A exact location or place. Usually
represented by a dot. It is important to
understand that a point is not a thing, No size.
We indicate the position of a point by placing a dot
with a pencil. This dot may have a diameter of,
say, 0.2mm, but a point has no size. Points are
usually named by using an upper-case single letter.
If a set of points all lie in a straight line, they are
called 'collinear'.
If a set of points all lie on the same plane, they are
called 'coplanar'.
Geometry
CH 1-2
Points Lines and Planes
Point: A exact location or place. Usually represented
by a dot. It is important to understand that a point is
not a thing, but a place.
Geometry
CH 1-2
Points Lines and Planes
Collinear: When a set of points all lie in a straight line.
Geometry
CH 1-2
Points Lines and Planes
Points that lie on the same line are collinear.
K, L, and M are collinear. K, L, and N are
noncollinear.
Points that lie on the same plane are
coplanar. Otherwise they are noncoplanar.
K
L M
N
Geometry
CH 1-2
Points Lines and Planes
Line: A geometrical object that is straight, infinitely
long and infinitely thin.
A line is one-dimensional. It has zero width. A straight
line is the shortest distance between any two points on
a plane.
Geometry
CH 1-2
Points Lines and Planes
Line: In the figure below, the line PQ passes through
the points P and Q, and goes off in both directions
forever, and is perfectly straight. A line, strictly
speaking, has no ends.
Geometry
CH 1-2
Points Lines and Planes
PLANE: A flat surface that is infinitely large and with
no thickness and extends forever.
It is difficult to draw planes, since the edges have to be
drawn. When you see a picture that represents a
plane, always remember that it actually has no edges,
and it is infinitely large.
point
line
Zero dimensions
One dimension
Plane
Solid
Two dimensions Three dimensions
Geometry
CH 1-2
Points Lines and Planes
Plane:
Geometry
CH 1-2
Points Lines and Planes
Plane:
Geometry
CH 1-2
Points Lines and Planes
Geometry
CH 1-2
Points Lines and Planes
Geometry
CH 1-2
Points Lines and Planes
TEACH! Example 1
Example 1: Naming Points, Lines, and Planes
A. Name four coplanar points.
A, B, C, D
B. Name three lines.
Possible answer: AE, BE, CE
Geometry
CH 1-2
Points Lines and Planes
Line Segment:
A straight line which links two points without extending
beyond them. A line segment is one-dimensional. It
has a measurable length, but has zero width..
The word 'segment' typically means 'a piece' of
something, and here it means the piece of a full line,
which would normally extend to infinity in both
directions.
Geometry
CH 1-2
Points Lines and Planes
Line Segment: See the figure below. The line
segment PQ links the points P and Q. The points P and
Q are called the 'endpoints' of the segment.
Geometry
CH 1-2
Points Lines and Planes
RAY:
A portion of a line which starts at a point and goes off
in a particular direction to infinity.
One way to think of a ray is a line with one end. A ray
starts at a given point and goes off in a certain
direction forever, to infinity.
The point where the ray starts is called (confusingly)
the endpoint. A ray has no measurable length, because
it goes on forever in one direction.
Geometry
CH 1-2
Points Lines and Planes
A Ray On its way to infinity it may pass through one or
more other points. In the figure above, the ray starts
at A and also passes through B..
Geometry
CH 1-2
Points Lines and Planes
Opposite Rays:
Opposite rays are two rays that both start from a
common point and go off in exactly opposite directions
and form a straight line.
You may name a ray using the Endpoint and any other
point which the ray passes through. Such as AB
Do not forget the ray crown 
Geometry
CH 1-2
Points Lines and Planes
Opposite Rays: When the two rays are opposite, the
points A,Q and B are collinear, and QA and QB form a
single straight line through the common endpoint Q...
Geometry
CH 1-2
Points Lines and Planes
Geometry
CH 1-2
Points Lines and Planes
Example 2: Drawing Segments and Rays
Draw and label each of the following.
A. a segment with endpoints M and N.
N
M
B. opposite rays with a common endpoint T.
T
Geometry
CH 1-2
Points Lines and Planes
TEACH! Example 2
Draw and label a ray with endpoint M that
contains N.
M
N
Geometry
CH 1-2
Points Lines and Planes
A postulate, is a statement that is accepted
as true without proof.
Postulates about points, lines, and planes
help describe geometric properties.
Geometry
CH 1-2
Points Lines and Planes
Geometry
CH 1-2
Points Lines and Planes
Geometry
CH 1-2
Points Lines and Planes
Example 3: Identifying Points and Lines in a Plane
Name a line that passes through two points.
XY
Geometry
CH 1-2
Points Lines and Planes
TEACH! Example 3
Name a plane that contains three noncollinear
points.
Possible answer: plane GHF
Geometry
CH 1-2
Points Lines and Planes
HINT
Use a dashed line to show the
hidden parts of any figure that
you are drawing. A dashed line
will indicate the part of the figure
that is not seen.
Geometry
CH 1-2
Points Lines and Planes
Example 4: Representing Intersections
A. Sketch two lines intersecting in exactly one
point.
B. Sketch a figure that shows a line that
lies in a plane.
Geometry
CH 1-2
Points Lines and Planes
TEACH! Example 4
Sketch a figure that shows two lines intersect
in one point in a plane, but only one of the
lines lies in the plane.
Geometry
CH 1-2
Points Lines and Planes
Lesson Quiz: Part I
1. Two opposite rays.
2. A point on BC.
3. The intersection of plane N and plane T.
4. A plane containing E, D, and B.
Geometry
CH 1-2
Points Lines and Planes
Lesson Quiz: Part II
Draw each of the following.
5. a line intersecting a plane at one point
6. a ray with endpoint P that passes through Q
Geometry
CH 1-2
Points Lines and Planes
Lesson Quiz: Part I
1. Two opposite rays.
CB and CD
2. A point on BC.
Possible answer: D
3. The intersection of plane N and plane T.
Possible answer: BD
4. A plane containing E, D, and B.
Plane T
Geometry
CH 1-2
Points Lines and Planes
Lesson Quiz: Part II
Draw each of the following.
5. a line intersecting a plane at one point
6. a ray with endpoint P that passes through Q
Geometry