Transcript Plane Geometry Unit 1 – Chapter 1

SECTION 1.1 NOTES
Undefined Terms – Vocabulary without a formal definition,
but overall agreement with what the term means.
Point – representation of a unique location in space. It has
no dimension.
P
Line – connection of an infinite number of points. It has one
dimension.
l
A
B
C
LINE NOTATION:
Line l, Line AB ( AB ), Line ( BC ),
or Line AC ( AC )
SECTION 1.1 NOTES
Compare and Contrast:
AB
Line – Infinite in length, extends endlessly in opposite
directions.
A
B
Segment – Finite portion of a line that begins and ends at
endpoints (points on that line).
A
AB
B
Ray – Infinitely long portion of a line that begins at an initial
point and extends endlessly in one direction.
Endpoint
A
B
AB
RAY NOTATION:
Point with no arrow head is called
endpoint, always list endpoint first and
always draw arrow pointing right.
SECTION 1.1 NOTES
Extension:
Opposite Rays – two rays that share the same endpoint but
extend in exactly opposite directions. They =alwys form a
straight line.
Endpoint
H
A
I
What are the opposite rays for the image given?
HA
HI
SECTION 1.1 NOTES
Plane – a flat surface that contains an infinite amount of
lines and extends endlessly in two directions.
M
W
C
O
PLANE NOTATION:
Plane M, or Plane COW,
Plane WOC, Plane OCW
PLANE NOTATION:
Use any three points that lie on the plane and that do
not lie in a line, or if a letter already represents it.
SECTION 1.1 NOTES
Collinear Points – points that all lie on the same line.
B
A
C
D
Coplanar Points – points that all lie on the same plane.
H
G
S
O
SECTION 1.1 NOTES
A
Identification, name:
The plane:
HOD, DOG, DGH
D
H
A Line:
AB, OB, HG, GO, …
O
A Segment:
GO, AO, BO, HG, …
G
A Ray:
OG, GH, BA, AB, HG, …
B
SECTION 1.1 NOTES
E
Identification, Collinear or not?
A) B, D
YES
B) C, E
YES
C) A, D
YES
D) B, F
YES
A
D
C
E) F, E, D NO
F) A, E, D NO
B
G) D, B, C YES
H) C, E, F YES
F
SECTION 1.1 NOTES
E
Identification, Coplanar or not?
A) B, C, D
YES
B) A, B, C
YES
C) F, E, D
YES
D) E, A, F
YES
E) A, B, C, D
YES
F) F, E, D, C
YES
G) E, A, D, C
NO
H) B, C, D, E, F YES
A
D
C
B
F
SECTION 1.1 NOTES
Intersections:
 2 lines always intersect at a point (Figure 1)
 A line that does not lie on a plane can intersect a plane at
a point. (Figure 2)
C Intersection
O
M
Figure 1
E
Intersection
P
C
W
Figure 2
F
SECTION 1.1 NOTES
Intersections: (cont.)
 2 Planes always intersect
at a line (Figure 3)
Intersection: Line a
a
M
Q
Figure 3
CHECK FOR UNDERSTANDING…TIME TO DRAW…
Four coplanar points…three or which are collinear.
A
D
C
B
CHECK FOR UNDERSTANDING…TIME TO DRAW…
Two coplanar lines that do NOT intersect.
F
B
E
C
H
D
CHECK FOR UNDERSTANDING…TIME TO DRAW…
Opposite rays AB and AC.
Endpoint
A
B
AB
C
AC
CHECK FOR UNDERSTANDING…TIME TO DRAW…
Three planes that do not intersect.
B
A
M
CHECK FOR UNDERSTANDING…TIME TO DRAW…
Three coplanar lines that intersect at the same
point.
B
F
E
B
H
E
C
D
CHECK FOR UNDERSTANDING…TIME TO DRAW…
Two planes that intersect one another.
a
M
Q
CHECK FOR UNDERSTANDING…TIME TO DRAW…
Two lines that intersect and a third line that does
not intersect either of them.
E
A
G
D
C
B
H
F
CHECK FOR UNDERSTANDING…TIME TO DRAW…
Three lines that intersect at a point but are not
coplanar.
A
D
H
O
F
G
B
CONCEPT CHECK
P. 3-5
#1 – 7
“Guided Practice”
HOMEWORK
P. 5-6
#3 - 26
(Omit #12)