1.1 Identifying Points, Lines, and Planes
Common words with no formal definition.
They form the foundation of other
formal definitions.
(location in space; has no dimension; represented by a dot)
(a set of points that extend in one dimension; length is infinite; no width; represented by a
line with an arrow on each end)
(two dimensional flat surface)
Undefined Terms:
Three most common undefined terms:PointLine
Plane
Point
Line Named by any two points on the line and a
line symbol. Can be named by a lower case cursive letter
and the word “line.”
N Point N
AB BC BD
ADACDCl
Line l
Named by one capital letter.
PlaneRepresented by a shape that looks like a wall or a floor,
or a parallelogram.
MA C
B
Can be named by one capital letter that doesn't represent a point.
Plane M
Can also be named by three points that are noncollinear.
Collinear Points lie on the same line.Plane ABC
Coplanar refers to points or lines that lie on the same plane.
The large red dots at the corners should not be pictured as they are not points.
They are a result of the program.
SOLUTION
EXAMPLE 1 Name points, lines, and planes
b. Name three points that are c. Name four points that are
• a. Other names for PQ are QP and line n. Other names for plane R are plane SVT and plane PTV.
a. Give two other names for PQ and for plane R.
b. Points S, P, and T lie on the same line, so they are collinear. c. Points S, P, T,and V lie in the same plane, so they are coplanar.
This page is to be copied if you can not correctly answer the questions.
Segments and RaysPart of a line. Two specific endpoints. Named by the two endpoints.
Part of a line with one endpoint. Named by the endpoint and any other point on the ray.
Two rays with the same endpoint. (Opposite halves of the same line.)
Line Segment
Ray
Opposite Rays
EXAMPLE 2 Name segments, rays, and opposite rays
b. Name all rays with endpoint J . Which of these rays are opposite rays?
SOLUTION
a. Another name for GH is
b. The rays with endpoint J are JE , JG , JF , and JH . The pairs of opposite rays with endpoint J are JE and JF , and JG and JH
.
a. Give another name for GH .
EXAMPLE 3 Sketch intersections of lines and planes
a. Sketch a plane and a line that is in the plane.
b. Sketch a plane and a line that does not intersect the plane.
c. Sketch a plane and a line that intersects the plane at a point.
SOLUTION
a b c
EXAMPLE 4 Sketch intersections of planes
Sketch two planes that intersect in a line.
SOLUTION
Draw: a second plane that is horizontal. Shade this plane a different color. Use dashed lines to show where one plane is hidden.
STEP 2
Draw: the line of STEP 3
Draw: a vertical plane. Shade the plane.
STEP 1
GUIDED PRACTICE for Examples 3 and 4
1. Sketch two different lines that intersect a plane at the same point.
ANSWER
GUIDED PRACTICE
6. Name the intersection of plane A and plane B.
7. Name the intersection of line k and plane A.
ANSWER Line K
ANSWER Line K
5. Name the intersection of PQ and line k.
ANSWER Point M
Use the diagram at the
Geometry Homework
Day 1 Page 5 (1-3, 5-11 odd, 12-16, 21-37odd, 40-43)
Day 2 worksheets
Sophomore Math!Page 5(1-31 odd, ! 40-42,47-58)
