Geometry Basics

Sections covered:

1.3 Points, Lines, & Planes

1.4 Segments, Rays, Parallel Lines, & Planes

Space

the set of all points

Points

location in space with no size, represented by a small dot and a letter

Line

series of points that extends in two opposite directions without endNamed:

AB

Collinear Points

points that lie on the same line

Example 1

Are points E, F, and C collinear?Are points E, F, and D collinear?

D

CE F

P

Plane

flat surface that has no thicknessThink of a sheet of paper

Coplanar

points and lines in the same plane

Example 2

Each surface of a cube represents part of a plane. Name the plane represented by the front of the cube.

E

A B

F

G

CD

H

Postulates & Axioms

Accepted statements of facts

We will use these in proofs to formulate ideas

Postulate 1-1

Through any two points there is exactly one line.

Postulate 1-2

If two lines intersect, then they intersect in exactly one point.

Postulate 1-3

If two planes intersect, then they intersect in exactly one line.

Example 3

What is the intersection of plane HGFE and plane BCGF?

E

A B

F

G

CD

H

Postulate 1-4

Through any three noncollinear points there is exactly one plane.

Example 4

Shade the plane that contains A, B, and C.

E

A B

F

G

CD

H

Example 4

Shade the plane that contains E, H, and C.

E

A B

F

G

CD

H

segment

part of a line consisting of two endpoints and all points between them

ray

part of a line consisting of one endpoint and all the points of the line on one side of the endpoint

opposite rays

two collinear rays with the same endpointalways form a line!

Example 5

Name all of the segments and rays in the figure:

L P Q

parallel lines

coplanar lines that do not intersect

skew lines

noncoplanar (not parallel and do not intersect)

Example 6

Name all segments parallel to DC.

Name all segments skew to DC.

N

J I

H

CD

G

M

A B

Parallel Planes

planes that do not intersect

a line and a plane that do not intersect are also parallel

Example 7

Use the diagram to name:two pairs of parallel planes

a line that is parallel to plane GHIJ

A

D

B

CI

H

J

G

Homework…

p. 19: 2-8 even, 14, 20, 38, 40, 50, 52, 55-60

p. 25: 12-23