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U SING U NDEFINED T ERMS AND D EFINITIONS. Point. A. A. A point has no dimension. . It is usually represented by a small dot. •. U SING U NDEFINED T ERMS AND D EFINITIONS. Line or AB. A line extends in one dimension. It is usually represented

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A point has no dimension

USING UNDEFINED TERMS AND DEFINITIONS

Point

A

A

A point has no dimension.

It is usually represented by a small dot.


A point has no dimension

USING UNDEFINED TERMS AND DEFINITIONS

Line or AB

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.

Collinear points are points that lie on the same line.


A point has no dimension

USING UNDEFINED TERMS AND DEFINITIONS

A plane extends in two dimensions. It is

usually represented by a shape that looks

like a table or a wall, however you must

imagine that the plane extends without end.


A point has no dimension

USING UNDEFINED TERMS AND DEFINITIONS

A

C

B

M

Coplanar points are points that lie on the same plane.

Plane M or plane ABC


A point has no dimension

Naming Collinear and Coplanar Points

H

G

F

E

D

• Name three points that are collinear.

• Name four points that are coplanar.

• Name three points that are not collinear.

SOLUTION

• Points D, E, F lie on the same line, so they are collinear.

• Points D, E, F, and G lie on the same plane, so they are coplanar.

Also, D, E, F, and H are coplanar.

• There are many correct answers. For instance, points H, E, and G do

not lie on the same line.


A point has no dimension

USING UNDEFINED TERMS AND DEFINITIONS

Another undefined concept in geometry is the idea thata point on a line is between two other points on the line.

You can use this idea to define other important termsin geometry.


A point has no dimension

USING UNDEFINED TERMS AND DEFINITIONS

Consider the lineAB (symbolized by AB).

The line segment or segmentAB

(symbolized by AB) consists of the

endpointsA and B, and all points on AB

that are between A and B.


A point has no dimension

USING UNDEFINED TERMS AND DEFINITIONS

Note that AB is the same as BA, and ABis the same as BA.

However, AB and BA are not the same.

They have different initial points and extend in different directions.

The rayAB (symbolized by AB) consists

of the initial pointA and all points on AB

that lie on the same side of A as point B.


A point has no dimension

USING UNDEFINED TERMS AND DEFINITIONS

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 plane. So, any two opposite rays are

collinear. Segments, rays, and lines are coplanar if they lie on the same plane.


A point has no dimension

Drawing Lines, Segments, and Rays

1

2

3

4

K

Draw JK.

J

Draw KL.

L

Draw LJ.

Draw three noncollinear points J, K, L. Then draw JK, KL and LJ.

SOLUTION

Draw J, K, and L


A point has no dimension

Drawing Opposite Rays

So, XM and XN are

opposite rays.

So, XP and XQ are opposite rays.

Draw two lines. Label points on the lines and name two

pairs of opposite rays.

SOLUTION

Points M, N, and X are

collinear and X is between

M and N.

Points P, Q, and X are collinear and X is between P and Q.


A point has no dimension

SKETCHING INTERSECTIONS OF 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.


A point has no dimension

Sketching Intersections

Sketch a line that intersects a plane at one point.

SOLUTION

Draw a plane and a line.

Emphasize the point

where they meet.

Dashes indicate where

the line is hidden by

the plane.


A point has no dimension

Sketching Intersections

Sketch two planes that intersect in a line.

SOLUTION

Draw two planes.

Emphasize the line where

they meet.

Dashes indicate where

one plane is hidden

by the other plane