Points, Lines, and Planes

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Points, Lines, and Planes

• The Three Undefined Terms of Geometry

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A point is an exact location in space.
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.
Point P
P
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Lines are 1-dimensional objects that have only
length. 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
B
Line AB
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A ray 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
D
Ray CD
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A line segment 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.
X
Y
Z
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Angles are defined by 3 points.
X
Y
Z
XYZ
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These angles can be right angles.
90 ?
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These angles can be right angles.
R
RST 90
USR 90
c
S
T
U
USV 90
TSV 90
V
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When lines intersect to form right angles, they
are said to be perpendicular.
R
UT
RV
c
S
T
U
V
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Lines can intersect to form acute and obtuse
angles.
45? acute
135? obtuse
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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 be parallel.
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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.Lets
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.
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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
skew
parallel
perpendicular
90º
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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
parallel
perpendicular
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The end.