1.3 Points, Lines, and Planes
“Dogs have owners. Cats have staff.”
-Dave Barry
Terms
A point is a location. It does not have a size.
Space is the set of all points.
A line is a series of points going in two opposite directions.
Points that lie on the same line are collinear (opp: noncollinear).
B
t
Are C, E, and F
collinear?
A
Name:
Are F, P, and D
collinear?
Terms
A plane is a surface that has no thickness. It contains many lines
going in all directions. A plane is named by one capital letter or at
least three of its noncollinear points.
B
P
A
C
Name:
Points and lines in the same plane are coplanar.
Terms
Figure on p.17
Name the plane represented by the front of the ice cube.
Name the plane represented by the bottom of the ice cube.
c
Postulates
A postulate is an accepted statement of fact.
Find the equation of the line through the points (0,1) and (1,3).
Postulate 1-1: Through any two points there
is exactly one line.
Line t is the only line that passes through points A and B
Postulates
Find the intersection of the following two lines.
y = -2x + 8
y = 3x - 7
Postulate 1-2: If two lines intersect, their intersection is exactly one
point.
c
Postulates
Postulate 1-3: If two planes intersect, their intersection is exactly one
line.
Plane RST and plane STW intersect in ST
Postulate 1-4: Through any three noncollinear points, there is exactly
one plane.
c
Examples
1) What is the intersection of plane
FGC and HDC?
2) Is D coplanar with H, G, and C?
3) Is A coplanar with F, C, and G?
4) Is C coplanar with H, E, and B?
1.3 Points, Lines, and Planes
HW: 4-14 EVEN, 18-24 EVEN, 38, 40, 4650, 65-67
Terms: point, space, line, collinear, plane, coplanar,
postulate, axiom
“Dogs have owners. Cats have staff.”
-Dave Barry