Transcript 1.1 Identify Points, Lines and Planes

1.1 Identify Points, Lines and Planes
•Undefined Terms (terms that do not have
formal definitions but have an understood
meaning)
Point
Line
Plane
1.1 Identify Points, Lines and Planes
Point: has no dimension. It is
represented by a dot.
 Line: has one dimension. It is
represented by a line with two
arrowheads, but it extends without end.
Plane: has two dimensions. It is
represented by a shape that looks like a
floor or a wall, but it extends w/o end.
1.1 Identify Points, Lines and Planes
 Collinear points are:
Points that lie on the same line.
Coplanar points are:
Points that lie on the same plane.
1.1 Identify Points, Lines and
Planes
Example 1:
a. Give two other names for Line PQ and
for plane R.
b. Name three points that are collinear and
Name four points that are coplanar.
1.1 Identify Points, Lines and Planes
 Defined terms: terms that can be described
using known words.
 Segment: the line segment AB, or segment
AB, consists of the endpoints A and B and
all the points that lie on line AB that are
between A and B.
 Ray: The ray AB consists of the endpoint A
and all the points on line AB that lie on the
same side of A as B.
1.1 Identify Points, Lines and Planes
If C lies on line AB between A and B, then
ray CA and ray CB are opposite rays.
Segments and rays are collinear if they lie
on the same line. So, opposite rays are
collinear. Lines, segments and rays are
coplanar if they lie on the same plane.
1.1 Identify Points, Lines and Planes
EXAMPLE 2:
a. Give another name for Segment PM.
b. Name all rays with endpoint Q. Which
of these rays are opposite rays?
1.1 Identify Points, Lines and Planes
Two or more geometric figures intersect if
they have one or more points in common.
The intersection of the figures is the set of
points the figures have in common.
The intersection of
two lines is a point.
The intersection of
two planes is a line.
1.1 Identify Points, Lines and Planes
Example 3:
a. Sketch a plane and two intersecting lines that
intersect the plane at separate points.
b. Sketch a plane and two intersecting lines that
do not intersect the plane.
c. Sketch a plane and two intersecting lines that
lie in the plane.
1.1 Identify Points, Lines and Planes
Example 3:
d. Sketch a plane and a line that is in the
plane.
e. Sketch two planes that do not intersect in
a line.
f. Sketch three lines that lie in a plane and
intersect at one point.
1.1 Identify Points, Lines and Planes
• Can two planes intersect in a segment?
Explain.
• Can a line intersect a plane in only two
points? Explain.