Lesson 1 -2

Points, Lines and Planes

Geometry Leeson: Undefined Terms, Lines, Line Segments

2

1) point

2) line

3) plane

The most fundamental concepts in geometry do not have precise definitions but, we understand their meanings intuitively. We say these concepts are undefined.

What are the undefined terms?

Geometry Leeson: Undefined Terms, Lines, Line Segments

3

A point indicates a position or location in space.

. P

X

Y

.

A(2,6)

Points are named using capital letters and/or coordinates.

Geometry Leeson: Undefined Terms, Lines, Line Segments

4

A line is an infinite set of adjacent points.Ex: Curved

line

Ex: Straight lineThe shortest distance between two points is a straight line.Naming a Line:

a) Two points on the line:

b) Single lowercase letter

m

, , , , ...AB AC BA BC etc-.-.-.-..-.-.-..-.-.-..-.-.-..-.-.-..-.-.-..-.-.-..-.-.-..-.-.-..-.-.-..-.-.-..-.-.-..-.-.-. .-.-.-.

A B C

m

5

A plane is a set of points that forms a completely flat surface. Two dimensions (length and width) Continues infinitely in all directions.Naming a Plane:

a) Four points on the plane:

(can name with 3 pts.)

b) Single uppercase letter:D

Plane ABCD

R

Plane R

BA

C

Space – the set of all points

Collinear points – points all in one line

Noncollinear – points not all in one line

Coplanar points – points all in one plane

Noncoplanar – points not all in one plane

Defined Terms

Intersection of two figures – set of all points in both figures

2lines intersect at a point

2 planes intersect at a line

3 planes intersect at a line or a point

A line intersects a plane at a point

INTERSECTS: meets or cuts

Geometry Leeson: Undefined Terms, Lines, Line Segments

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Def: Collinear Points:A collinear set of points is a set of points all of which lie on the same straight line.

A B C D

E

•Points A, B, C and D are collinear.

•Points A, E and C are not collinear.

Draw and label a picture of intersecting lines.

Drawing

Draw and label two planes that intersect in a line.

Drawing

Draw a line intersecting a plane in exactly one point.

Drawing

Draw two parallel planes.

Are all horizontal planes parallel to one another?

Are all vertical planes parallel to one another?

Drawing

DrawingDraw two vertical planes that are parallel to each other.

Draw to parallel planes that are not parallel to each other.