1.2 points, lines and planes. using undefined terms and definition a point has no dimension. it is...
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1.2 Points, Lines and Planes
Using Undefined terms and definition
• A point has no dimension. It is usually represented by a small dot.
A
Point A
Using Undefined terms and definition
• A line extends in one dimension. It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions.
A
B
l
Line l or AB
Name that line
Using Undefined terms and definition
A plane extends in two dimensions. It is usually represented by a shape that looks like a tabletop or wall. You must imagine that the plane extends without end even though the drawing of a plane appears to have edges.
A
BC
M
Plane M or plane ABC
Name that Plane
A few basic concepts . . .
Collinear points are points that lie on the same line.
Non-Collinear points are points that do not lie on the same line.
Coplanar points are points that lie on the same plane.
Non-Coplanar points are points that lie on the same plane.
Ex. 1: Naming Collinear and Coplanar Points
a. Name three points that are collinear
G
D E F
H
Ex. 1: Naming Collinear and Coplanar Points
b. Name four points that are coplanar. G
D E F
H
Ex. 1: Naming Collinear and Coplanar Points
c. Name three points that are not collinear.
G
D E F
H
More . . . The line segment
or segment AB (symbolized by AB) consists of the endpoints A and B, and all points on AB that are between A and B.
l
Line l or AB
A
A
B
B
Segment AB
More . . .
The ray AB (symbolized by AB) consists of the initial point A and all points on AB that lie on the same side of A as point B.
l
Line l or AB
A
A
B
B
Ray AB
More . . . Note that line AB
is the same as line BA However, ray AB and ray BA are not the same. They have different initial points and extend in different directions.
l
Line l or AB
A
A
B
B
Ray BA
More . . .
If C is between A and B, then CA and CB are opposite rays.
Like points, segments and rays are collinear if they lie on the same line. So, any two opposite rays are collinear. Segments, rays and lines are coplanar if they lie on the same plane.
l
Line l or AB
A
C
B
Ex. 2: Drawing lines, segments and rays
Draw three noncollinear points J, K,
and L. Then draw JK, KL and LJ.
J
K
L
Draw J, K and L
Then draw JK
Ex. 2: Drawing lines, segments and rays
Draw three noncollinear points J, K,
and L. Then draw JK, KL and LJ.
J
K
L
Draw KL
Ex. 2: Drawing lines, segments and rays
Draw three noncollinear points J, K,
and L. Then draw JK, KL and LJ.
J
K
L
Draw LJ
Ex. 3: Drawing Opposite Rays Draw two lines.
Label points on the lines and name two pairs of opposite rays.
P
MQ
N
X
Ex. 3: Drawing Opposite Rays Draw two lines.
Label points on the lines and name two pairs of opposite rays.
P
MQ
N
X
Ex. 4: Sketching intersections
Sketch the figure described.
a. A line that intersects a plane in one point
Draw a plane and a line.
Emphasize the point where they meet.
Dashes indicate where the line is hidden by the plane
Ex. 4: Sketching intersections Sketch the figure
described.b. Two planes that
intersect in a line Draw two planes. Emphasize the line
where they meet. Dashes indicate
where one plane is hidden by the other plane.
Practice
Practice