Points, Lines, Planes and Angles

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Points, Lines, Planes and Angles
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Objectives

• Students will be able to
• Define Point, line, plane, collinear, coplanar,
  line segment, ray, intersect, intersection
• Name collinear and coplanar points
• Draw lines, line segments, and rays
• With proper labeling
• Draw opposite rays
• Sketch intersections of lines and planes and two
  planes

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Common Words

• What are common words we use in everyday
  conversation?
• Do you have to think about their meanings?
• What if you didnt know these words?
• In todays lesson you will learn about common
  words needed to speak the language of geometry.

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Points, Lines, and Planes
A

• A location in space, but has no size or shape

Point
Called Point A
Extends without end in one dimension (two
directions) and always straight
Line
l
Z
Y
Or line l
Called
Plane
Extends without end in two dimensions (all
directions), always flat, and has no thickness
A
C
B
Called plane ABC or plane M
M
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Space
What is Space?
The set of all points.
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Collinear and Coplanar
Collinear

• Points on the same line

G
F
E
D
Points
D, E, F, and G are collinear
Coplanar
B
A
C
n
A, B, and C are coplanar points
l
Lines l and n are coplanar lines
Co means
together
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Naming Points

• Name a point that is collinear with the given
  points

A
C
B
B and E
I
F
E
C and H
D
E
D and G
B
I
A and C
H
B
G
H and E
C
G and B
D
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Example 1 Naming Points
Three points that are collinear
H
P
G
D, E, F
F
E
D
Four points that are Coplanar
D, E, F, G and D, E, F, H (plane not shown)
Three points that are not collinear
H, E, G
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Naming Points
Name a point that is coplanar with the given
points or not coplanar
M, N, R
T
O
S
P
M, N, O
P
P, O, R
T
Q
T, Q, N
O
N
R
T, S, R
Q
Q, S, O
P
M
T
P
M, T, Q
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Line Segments and Rays
End points Y and Z and all points in between
Line Segment
Y
A
Z
Line YZ
Line segment
Y
A
Z
AZ
YA,
YZ,
YZ
YA
AZ
Ray
Starting point and all points that extend from
that point
B
A
Ray AB
AB
B
A
Ray BA
BA
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Drawing Lines and Rays

• Draw Points J, K, and L (non-Collinear)

Then, draw JK, KL, and LJ try connecting
them all
J
L
K
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Intersections
Intersect

• To cross at a common point.

(verb)
k
Lines k and l intersect at the point A, so both
lines have this point in common.
A
l
A set of points that are shared between two lines
or planes
Intersection
(noun)
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Postulate 1-3
If two planes intersect, then they intersect in
exactly one line.
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A set of points that are shared between two
lines or planes

• Intersection

n
T
P
line n and plane P intersect at point T
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• VISUALIZATION Name the geometric shape modeled
  by a colored dot on a map used to mark the
  location of a city.

A. point B. line segment C. plane D. none of the
above
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VISUALIZATION Name the geometric shape modeled
by the ceiling of your classroom. (In this
particular case, it doesnt extend forever)
A. point B. line segment C. plane D. none of the
above
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Choose the best diagram for the given
relationship. Plane D contains line a, line m,
and line t, with all three lines intersecting at
point Z. Also point F is on plane D and is not
collinear with any of the three given lines.
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Interpret Drawings
How many planes appear in this figure?
Answer There are two planes plane S and plane
ABC.
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Postulate 1-1

• Through any two points there is exactly one line.

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Postulate 1-2

• If two lines intersect, then they intersect in
  exactly one point.

A
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Postulate 1-4
Through any three non-collinear points there is
exactly one plane.
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Points Y, Z, and W lie on a line, so they are
collinear.
Any other set of three points do not lie on a
line, so no other set of three points is
collinear.
For example, X, Y, and Z and X, W, and Z form
triangles and are not collinear.
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You can name a plane using any three or more
points on that plane that are not collinear.
Some possible names for the plane shown are the
following
plane RST
plane RSU
plane RTU
plane STU
plane RSTU
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(No Transcript)
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As you look at the cube, the front face is on
plane AEFB, the back face is on plane HGC, and
the left face is on plane AED.
Planes HGC and AED intersect vertically at HD.
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Closure

• Name five of the nine common words we learned

How far does a line go in each direction? A
plane?
How many directions does a ray have?
What is it called when points are on the same
line? In the same plane?
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Make a Conjecture
a) Make a conjecture in terms of Q(n) for the
following sequence, b) find the 100th term.
N 1 2 3 4 5
Q 5 7 9 11 13
a) 2n 3
b) 203