Understanding Points, Lines, and Planes
section 1-1
GEOMETRY
geo - earth; metry - measurement
The most basic figures in Geometry are undefined terms, which can't be defined
by using other figures. These basic building blocks of Geometry include the terms
point, line, and plane.
* The remaining terms that we use in Geometry this year will be defined terms.
collinear points - points that lie on the same line
coplanar points - points that lie in the same plane
problem # 1 - In the figure below, name the following:
a. the blue line in 4 different ways
b. two collinear points
c. two noncollinear points (be careful)
d. three noncollinear points
e. a ray with endpoint at B
f. two opposite rays
A
B
E
C
j
D
intersection - the set of all points that two or more figures have in common
problem # 2 - In the figure below, name the following:
a. the orange plane in two different ways
b. three coplanar points
c. three noncoplanar points (be careful)
d. four noncoplanar points
e. the intersection of the two planes
R
C
Y
M
A
E
B
X
D
* Dotted lines in a figure indicate parts hidden from view.
postulate (axiom) - a statement that is accepted as true without proof
** Real-life application of theorem 1-1-2 - three-legged stool / tripod
* see next page for pictures
problem # 3 - In the figure below, name the following:
a. a line that is contained in plane M
b. a line that passes through plane M (and is not contained)
c. two coplanar lines that intersect
d. the intersection of two noncoplanar lines
m
M
A
R
j
P
k
problem # 4 - Sketch each of the following figures:
a. two lines that intersect in one point in a plane, but only one
of the lines lies in the plane
b. two vertical planes intersecting in a line
c. one vertical plane and one horizontal plane intersecting in
a line
* See the next page for sample diagrams.
Applications of theorem 1-1-2
Milking Stool
Tripod with Telescope
Tripod Table
Tripod with Gun
Answers to problem # 4:
j
a.
k
P
M
k
R
M
b.
R
M
M
c.
k
R