Transcript 1.2 Points, Lines, & Planes

Points, Lines, & Planes
What is a definition?
• Known words used to describe a new
word
Undefined terms – not formally defined
There are 3 in geometry.
Point
Line
Plane
Point
1. Has no dimension (no length, width,
thickness)
2. Usually represented by a dot
3. Named using one capital letter
• B
Line
1. Extends forever in one dimension (length)
2. Has an arrowhead on each end
representing the fact that it goes on
forever
3. Consists of an infinite amount of points
4. Always straight
5. Named with a lowercase script letter or by
Can be called:
2 points on the line
l
A
B
Line l
Line AB or AB
Line BA or BA
Plane
1. Extends forever in 2 dimensions (length &
width)
2. A flat surface consisting of infinitely many
points
3. Usually represented by a 4-sided figure
4. Named with a capital script letter or 3
points on the surface of the plane
W
A
B
C
Can be named:
Plane W
Plane ABC, plane BCA, plane
CBA, etc.
More Definitions
• Collinear points –
points that lie on the same line
• Coplanar points –
points that lie on the same plane
Line Segment (or segment)
• A section of a line that has 2 endpoints
A
B
• Named by its endpoints. AB or BA
Ray
• Piece of a line with only one endpoint
(initial point) and continues forever in the
other direction
B
A
• Named by the endpoint and a second point
named on the ray. (name MUST begin with
the endpoint!)
AB
Opposite Rays
• 2 rays that share a common initial point
and face opposite directions.
P
Q
S
• QP and QS are opposite rays.
Example: 6 volunteers please!
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Draw & label points A & B.
Draw & label points C & D.
Draw AB.
Draw BC.
Draw AC.
Draw DA.
More Definitions
• Intersect –
2 or more figures intersect if they
have one or more points in common.
• Intersection –
all points or sets of points the
figures have in common
• What is the intersection of:
AB & DA
BC & AC
BC & BC
When 2 planes intersect,
their intersection is a line.
Assignment