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Section 1.2Points, Lines, & Planes
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What is a Point?2/17
What is a Line?3/17
What is a Plane?4/17
Representations of Points
A point is the most basic building block of geometry.
A point indicates a location.
A dot represents or models a point.
A point is named with a capital letter.
A
B
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Representations of Lines
A line is a one dimensional object that extends indefinitely in two directions
A line may be named with two identified points on the line.
A line symbol (double-headed arrows) is placed over the letters naming the points on the line.
Alternatively, line may be named with a single, lower case letter.
Q SRead it as:
“Line QS” or “Line SQ”
Write it as:QS
or SQ
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Representations of Planes
A plane has length and width but no thickness.
In the figure at the right, the flat surface represents a portion of plane Q.
A plane may also be named using three points that lie in the plane, such as G, F and E; please note that the three points are not on the same line (Plane GFE).
Q
G
E
F
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Representations of Rays
A ray is a part of a line that starts at a point and extends infinitely in one direction.
The point is called the
endpoint of the ray.
A ray is named its endpoint first.
A single arrow (toward the infinite direction) is drawn over the two capitalized letters.
C DRead it as: “Ray CD” (the order does matter)
Write it as:
CD
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Representations of Rays
All Opposite Rays
• Share exactly one point• Form a line• In Opposite Directions
C, D & F are collinear and D is between C & F.
C D F
DC
DF
Yes
DC
CD
No
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Representations of Segments
A segment is a part of a line that begins at one point and ends at another.
The points are called the
endpoints of the segment.
A segment is named by its endpoints.
A bar (no arrows) is drawn over the two capitalized letters.
R BRead it as:
“Segment RB” or “Segment BR”
Write it as:RB
or BR
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Interactions between Points, Lines, & Planes
Collinear points are points that lie on the same line.
In the figure at the right, C, D and F are collinear.
C, D and E are non-collinear (not collinear).
Any two points are collinear.
C D
E
F
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Interactions between Points, Lines, & Planes
Coplanar points are points that lie in the same plane.
In the figure at the right, E, F, G, and H are coplanar.
E, F, G, and J are non-coplanar (not coplanar).
Any three points are coplanar.
Q
G
E
FH
J
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Interactions between Points, Lines, & Planes
The intersection of two lines is a
___________.
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Interactions between Points, Lines, & Planes
The intersection of two planes is
a ___________.
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Interactions between Points, Lines, & Planes
Through any three non-collinear points there is exactly one
_______________.
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A Few Questions
GD
E F
H
M
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HOMEWORK 1.2
P.13 1 – 8, 28, 29, 34, 35, 36, 48, 73 – 75
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