The Building Blocks of Geometry
• Points
• Line
• Plane
Q: These terms are called undefined
terms. Why?
1
In geometry, definitions are formed using
known words or terms to describe a new
word. A formal definition states what the
term being defined is and how it differs from
others like it. There are three words in
geometry that are not formally defined, but
there is an agreement about what they
mean. These three undefined terms are
point, line and plane.
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Points
Point - a location in space. It has no size. It is
named by a capital letter.
.
A
Points are usually
represented with a
capital letter, but in the
coordinate plane a
point is represented as
an ordered pair (x,y).
Points
Can anyone identify examples of points in the real world?
4
Lines
line - a series of points that extends in two
opposing directions without end. Lines have
no thickness.
Q
S
Lines can be represented by two points on the line.
Example:
QS or SQ
On the coordinate plane a line could be represented
as an equation relating a set of points.
Lines
Write the equation of a line through the points D(2, 9) and
C(-3, 24). Also, represent it symbolically (not graphically).
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Line Segments
Line segment - a part of a line with two
endpoints.
B
R
A segment is named by its endpoints.
Example: RB
or
BR
Line Segments
Why is a line segment a defined term if a line is
considered undefined?
8
Rays
Ray - consists of an endpoint and all the points
of a line on one side of the endpoint.
C
D
Read it as: “Ray CD”
(the order does
matter)
Write it as: CD
True or false, ray NQ has another name. If
true, what is the name?
Name a pair of opposite rays.
10
Planes
plane - a flat surface with no thickness that
extends without end in all directions.
http://www.mathsisfun.com/geometry/plane.
html
What is wrong geometrically with the .gif in
the link above?
11
Identify which of the following apply.
When two planes intersect, ____ line(s) are
formed.
0
1
2
3
Infinity
12
True or False:
If two lines do not intersect, then they are
parallel.
If two lines are parallel, then they do not
intersect.
If two lines intersect, then they are not
parallel.
Hint: Look for counterexamples (they fit the first
part of the statement but not the second). 13
Planes
Intersecting lines - cross (intersect) at exactly
one point.
Parallel lines – do not intersect, but on the
same plane.
Skew lines – do not intersect, but are on a
different plane.
• Collinear Points
• Coplanar points
• Opposite rays
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• Collinear Points - points that lie on the
same line.
• Coplanar points - points that lie in the
same plane.
• Opposite rays - 2 rays that lie on the same
line, with a common endpoint and no other
points in common. Opposite rays form a
straight line and/or a straight angle (180°:).
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Congruent Segments
Two segments are congruent if and only if
they have equal lengths. You can show two
segments are congruent by making identical
markings.
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Group Investigation
With your partner…
Look around the classroom and identify
examples of each of these terms: point, line,
plane, line segment, congruent segments,
midpoint of a segment, parallel line
segments and ray.
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