Cover Slide
Identifying Points, Lines
And Planes
3 Undefined Terms
Points, Lines, and Planes
The 3 Undefined Terms of Geometry
Points, Lines, and Planes
• undefined geometric terms
• described instead of defined• a starting “point” for us to build on• used in the definitions of more complex geometric figures
• three most basic figures in geometry
Points
Points, Lines, and Planes
Points
Examples: a dot or a star
Named: usually by a capital letter
A
B
C Points A, B and C
• no actual size• sometimes represented by objects that do have size• all geometric figures are composed of points
Lines
Points, Lines, and Planes
Named: usually by a lower-case letter (sometimes script)by any two points on the line and the line symbol
Example: the dotted lines on a street or highway
or
b
bE
Dline DEline ED
DEED
• series of points extending indefinitely in two directions• no thickness or width• represented by a figure that does have thickness
Ways to namethe line to the left:
Lines
Planes
Points, Lines, and Planes
Example: a ceiling or a wall
Named: usually by a capital letter (sometimes script)by any three points that are not on the same line but are in that plane
or
K
plane RST
Planes• a flat surface• no thickness or width• extends indefinitely in all directions
Ways to name the plane to the right:
KR S
T
Collinear/Noncollinear
Definitions
Collinear• points that lie on the same line
Noncollinear• points that do not lie on the same line
CB
DB, C, and D are collinear
E
FGE, F, and G are noncollinear
One line could not pass through all 3 points.
Coplanar/Noncoplanar
Definitions
Coplanar• points that lie in the same plane
Noncoplanar
• points that do not lie in the same plane
CB D
A, B, C, and D are coplanar
E F
GE, F, G, and H are noncoplanar
A
H
Space/Intersection
Definitions
Space
Intersection• the intersection of two figures is the set of points that are in both figures
• the set of all points• three-dimensional • points, lines, and planes are contained in space
Some examples of intersection will be demonstrated on the following slides.
Relation line-point, 2 lines
Point, Line, and Plane - Relationships
S
R
d
a b
S is on d. S is in d.
d passes through S.d contains S.
The intersection of d and S is S.
The intersection of a and b is R.
a and b intersect at R.
a and b intersect in R.
both a and b contain R.
Relation line-plane, 2 planes
Point, Line, and Plane - Relationships
b and D are in W. W contains b and D.
The intersection of a and W is D.
C
B
X
Y
a intersects W at D. D
W
b
a
a and b do not intersect.
BC is in Y and X. Y and X both contain BC.
Y and X intersect in BC.
All points on BC are in Y and X.The intersection of Y and X is BC.
Q & A prob. 1-6 (T or F)
Q & A
A
B
C
D
E
H
F
NJ
KL
M
Determine whether each statement is
true or false.
1.
2.
3.
4.
5.
6.
A, M, and C are collinear.
F, L, B, and C are coplanar.
D, M, and B are coplanar.
A, C, and E are collinear.
E, L, K, and B are coplanar.
A, C, and E are coplanar.
true
true
false
false
true
true
Q & A prob. 1-5
Q & A
A
B
C
D
E
H
F
NJ
KL
M
Refer to the figure at the left to answer each question.
B
planes BDH & EDH
C, K
planes FAD, FED, BND
C
1.
2.
3.
4.
5.
Name 3 planes thatintersect at D.
Name all points coplanarwith E, H, and B.
Name the intersection ofBC and NB.
Name two planes thatintersect in DH.
Name the intersectionof BC and plane EFA.