definitions goals understand and use the basic undefined and defined terms in geometry sketch the...
TRANSCRIPT
DefinitionsDefinitions
Goals
•Understand and use the basic undefined and defined
terms in geometry
•Sketch the intersection of lines and planes
Academic Geometry: Chapter 1
Conjecture – an unproven statement that is based on observations
_________________– process of looking for patterns and making conjectures
•To prove a conjecture is ______ – you must prove that it is
true for ____ cases.
•To prove a conjecture is ______ – you must prove it is false
for just ____ case.Example:
Conjecture: If you are taking geometry, then you must be a sophomore
True or False
.____________________
_______________ – an example that shows a conjecture is false.
Point: •Has no dimension
•Represents a location in space
•Represented by a small dot
•Named using a capital letter
APoint A
Line:
•Has one dimension - length
•Extends infinitely in opposite directions
•Named using two points on the line or
scripted letter
B L U E
Name the following line as many ways as possible:
BL BU BE LU LE UE
A Bc
ABSymbol: Or line c
Plane
•_________________________
•_____________________
•_________________________
•_________________________
_________________________ A
B
C
M
Plane ABC or plane M
__________________
_______– Points that lie on the same line
__________________
_______– Points that lie on the same plane
_______________________
__– Points that do not lie on the same plane
________________________
_– Points that do not lie on the same line
Why do we need to use three non- collinear points when naming a plane?
A B
C
DE
FG H
I
Place your pencil on Plane ABH.
Top of the box.
Place your pencil on Plane BHC.
Right side of the box.
Place your pencil on Plane FGH.
Is it the top or the front?
Place your pencil on Plane HID.
Is it the front or the right side?
Line segment or segment:
•Has one dimension - length
•Is part of a line
•Has endpoints – a beginning and an end
•Named using its endpoints
Q R
QRSymbol:
A B C D
Name each of the segments in the following figure:
______________________________________
Ray
•Has one dimension - length
•Is part of a line
•Has one endpoint
•Extends infinitely in one direction
•Named using its endpoint first and then
another point on the ray
F B
FBSymbol:
A YR M
What are all the ways that the whole ray can be named?
Is AM the same as RM? No – different starting point
Opposite Rays
•Rays which share the same endpoint
and extend in opposite directions
•Any two opposite rays are collinear
A B C
BA and BC are opposite rays
Are BC and CB opposite rays?
No – different starting points
Intersect
•Two or more geometric figures intersect if
they have one or more points in common
•Where figures come together
Line 1
Line 2
Intersection
B
D
A
F
C
H
E
G
•What is created by the intersection of two lines?
_______
•What is created when two planes intersect?
______
•Name two planes that intersect and the line that
their intersection makes.
Plane DCB and Plane CBF create ____
Plane DCG and Plane EFG create____
Intersection (continued)
B
D
A
F
C
H
E
G
•What is created when three planes
intersect each other?
•Is it possible for two planes not to intersect?
If yes, name two that do not intersect.
Plane EFG and Plane ABC
Plane ADH and Plane FGC
Planes ABC, BCF, and GDH intersect at…?
__________
B
D
A
F
C
H
E
G
Are points A , B , and G on the same plane?
______
B
D
A
F
C
H
E
G
Parallel Lines:
_________________________ _________________________
Skew Lines:
_________________________ _________________________