Download - Introduction to Geometry by Samuel Chukwuemeka (Samdom For Peace) Points, Lines, and Planes
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Introduction to Geometryby
Samuel Chukwuemeka(Samdom For Peace)
Points, Lines, and Planes
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A point is an exact location in space. It has no size.
You are here.
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A true point has no length, no width, and no height.
In fact, you cannot see a true point.
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A point is named by a letter.
P
Point P
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Lines are series of points that extends in opposite directions without end. Lines continue forever in both directions.
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Because a line has no width or height, you cannot see a true line.
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A line is defined by 2 points.
A
BLine AB
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A ray is part of a line that has a starting point but no ending point.
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A ray of light has a starting point (like the sun) and continues
forever in the same direction.
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Of course, if the ray hits an object, the light could be
absorbed or reflected.
MIRROR
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A ray is also defined by 2 points.
C
DRay CD
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A line segment is part of a line that has a starting point and an
ending point. Line segments can be measured.
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A line segment also defined by 2 points.
E
F Line Segment EF
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Lines can do various things.
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Lines can intersect at a point to form angles. Two lines intersect if they have exactly one point in common. Lines
that intersect are called Intersecting Lines.
X
Y
Z
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So, an Angle is formed when two lines meet or intersect. Angles are defined by 3 points.
X
Z
Y
XYZ
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These angles can be right angles.
90
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These angles can be right angles.
c
R
S TU
V
m RST = 90⁰m USR = 90⁰
m USV = 90⁰ m TSV = 90⁰
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When lines intersect to form right angles, they are said to be perpendicular.
V
R
TU
cS
UT RV
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Lines can also intersect to form acute and obtuse angles.
135
obtuse
45 acute
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Lines can also run into each other to form straight angles.
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180 is a straight angle
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Lines do not always intersect.
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Lines can also be parallel. Parallel lines are lines that lie on the same plane and do not intersect.
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Parallel lines have the same slope or steepness.
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Is it possible for lines not to intersect and not be parallel
either?
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Believe it or not, this is possible.Let’s consider a 3-dimensional
rectangular prism.
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These 2 lines are not parallel, but they are not intersecting either.
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These lines are called skew lines. Skew lines are lines that do not lie in the same plane and do not intersect.
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You might have heard the word “skewer” the last time you had a
barbecue.
S
K
E
W
E
R
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A skewer raises your “dinner” off the surface of the grill. The skewer does not intersect the grill, and the skewer is not
parallel to the grill.
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Lines can be…
intersecting
perpendicular
90º
parallelskew
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A plane
is a flat
surface that has
length & width
but no height.
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You can see a plane only if you view it at a certain angle.
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A true plane goes on forever in all directions.
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A true plane goes on forever in all directions.
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A true plane goes on forever in all directions.
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A true plane goes on forever in all directions.
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A true plane goes on forever in all directions.
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Planes can…
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Planes can intersect.
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An X-Wing fighter from Star Wars has wings that intersect.
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Planes can be perpendicular.
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Planes can be parallel.
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A Tie Fighter from Star Wars has wings that are parallel.
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Planes can be…intersecting
perpendicular
parallel
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Assignment
In a tabular form,
(1.) Differentiate between a point, a line, a plane, a segment, and a ray.
(2.) Differentiate between intersecting, parallel, and skew lines
(3.) Define a perpendicular line
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Sweethearts and Gentlemen, ask your questions.