Download Collinear points

UNDERSTANDING POINTS, LINES,
AND PLANES (TERMS)
GEOMETRY H2 (HOLT 1-1A)
K. SANTOS
GEOMETRY
• Geo---means “earth”
ex: geography, geology
• Metre—means “to measure”
ex: meter
• Geometry----measuring the Earth
GEOMETRY
Euclid
Father of Geometry
Elements
Different Types of Geometry
We study Euclidean Geometry
Other types—Noneuclidean Geometry
Hyperbolic
Elliptical
THREE UNDEFINED TERMS
• Point
• Line
• Plane
we can describe these terms but be cannot
define them
POINT
•
•
•
•
•
Names a location
Has no size or thickness
Represented by a small dot
Named by one capital letter
A geometric figure is a set of points
•A
named as A
LINE
• Series of points that extends (infinitely) in two opposite
directions
• Straight path
• Contains an infinite number of points
• Has no thickness
• Can be named by any two points on the line (2 capital
letters)
• Can be named by one lowercase letter (not a point)
A
𝐴𝐵 or 𝐵𝐴
x
B
line x
PLANE
• Flat surface that continues in all directions without
end (extends forever)
• It can be drawn with sides but it has no boundaries
• Has no thickness
• Name by at least three points that are not collinear
(three or more capital letters)
• Or named by one capital letter (usually script)that is
not a point usually the letter is found in corner of the
diagram
• Think of it as a piece of paper that continues out in
all directions
PLANE (CONTINUED)
COLLINEAR AND NONCOLLINEAR
POINTS
• Collinear points--Points (3 or more) that lie on the
same line
• Noncollinear points--three or more points that can
not be connected by a straight line (at least one
point isn’t in line with the others)
H
Collinear points: H, I and J
G
I
Noncollinear points:
J
G, H and I
COPLANAR AND NONCOPLANAR
POINTS
• Coplanar points--four or more points in the same
plane
ex. Four points (things) on the same wall
• Noncoplanar points--four or more points that are
not in the same plane (just need one point not on
the same plane)
ex: Four points (things) where three are on the
same wall and the fourth is on a different
wall
SEGMENT (LINE SEGMENT)
• Is part of a line consisting of two points and all the
points between them
• Still has an infinite number of points
• Named by the two endpoints (capital letters)
M
N
O
𝑀𝑂
or 𝑂𝑀
ENDPOINT
• A point at one end of a segment or the starting
point of a ray
M
N
𝑀𝑁 has endpoints M and N
RAY
• The part of the line consisting of one endpoint and
all the points of the line on one sides of the endpoint
• still contains an infinite number of points
• Named by two capital letters
• First letter is the endpoint
• Second letter is for a point the ray passes through
• Think of a ray of sunshine
K
J
I
𝐾𝐽 or𝐾𝐼
OPPOSITE RAYS
• Two collinear rays with the same endpoint
• Two opposite rays always form a line
A
B
C
The opposite rays are 𝐵𝐴 and 𝐵𝐶