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Points, Lines, and Planes

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Points, Lines, and Planes The Three Undefined Terms of Geometry You can see a plane only if you view it at a certain angle. A true plane goes on forever in all ... – PowerPoint PPT presentation

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Title: Points, Lines, and Planes


1
Points, Lines, and Planes
  • The Three Undefined Terms of Geometry

2
A point is an exact location in space.
You are here.
3
A true point has no length, no width, and no
height.
In fact, you cannot see a true point.
4
A point is named by a letter.
Point P
P
5
Lines are 1-dimensional objects that have only
length. Lines continue forever in both
directions.
6
Because a line has no width or height, you cannot
see a true line.
7
A line is defined by 2 points.
A
B
Line AB
8
A ray has a starting point but no ending point.
9
A ray of light has a starting point (like the
sun) and continues forever in the same direction.
10
Of course, if the ray hits an object, the light
could be absorbed or reflected.
MIRROR
11
A ray is also defined by 2 points.
C
D
Ray CD
12
A line segment has a starting point and an ending
point. Line segments can be measured.
13
A line segment also defined by 2 points.
E
F
Line Segment EF
14
Lines can do various things.
15
Lines can intersect at a point to form angles.
X
Y
Z
16
Angles are defined by 3 points.
X
Y
Z
XYZ
17
These angles can be right angles.
90 ?
18
These angles can be right angles.
R
RST 90
USR 90
c
S
T
U
USV 90
TSV 90
V
19
When lines intersect to form right angles, they
are said to be perpendicular.
R
UT
RV
c
S
T
U
V
20
Lines can intersect to form acute and obtuse
angles.
45? acute
135? obtuse
21
Lines can also run into each other to form
straight angles.
22
180 ? is a straight angle
23
Lines do not always intersect.
24
Lines can be parallel.
25
Parallel lines have the same slope or steepness.
26
Is it possible for lines not to intersect and not
be parallel either?
27
Believe it or not, this is possible. Lets
consider a 3-dimensional rectangular prism.
28
These 2 lines are not parallel, but they are not
intersecting either.
29
These lines are called skew lines.
30
You might have heard the word skewer the last
time you had a barbecue.
S K E W E R
31
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.
32
Lines can be
intersecting
skew
parallel
perpendicular
90º
33
A plane
is a flat
surface that has
length width
but no height.
34
You can see a plane only if you view it at a
certain angle.
35
A true plane goes on forever in all directions.
36
A true plane goes on forever in all directions.
37
A true plane goes on forever in all directions.
38
A true plane goes on forever in all directions.
39
A true plane goes on forever in all directions.
40
Planes can
41
Planes can
intersect.
42
An X-Wing fighter from Star Wars has wings that
intersect.
43
Planes can
be perpendicular.
44
Planes can
be parallel.
45
A Tie Fighter from Star Wars has wings that are
parallel.
46
Planes can be
intersecting
parallel
perpendicular
47
The end.
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