Applied GeometryLesson 1-2

Points, Lines, and Planes

Objective:Learn to identify and draw models of points, lines, and planes,

and determine their characteristics.

Point – the basic unit of geometry

Has no size

Named using CAPITAL Letters

Read as point A

Line – a series of points that extends without end in two

directions.

Made up of an infinite number of points

Arrows show that the line extends without end in both directions

Named: either a single lowercase script letter OR 2 points on the line

Named: line l or BAAB,

Example 1

Name two points on line mGive 3 names for the line

point P and point Q (or Point R)

RQPRQPQRRPPQm ,,,,,,

Definitions

Collinear – points that lie on the same line

Noncollinear – points that do not lie on the same line.

Example 3

Name three points that are collinear and three points that are noncollinear.

Collinear – A, B, E or D, B, CNoncollinear – A, B, D or C, B, E or A, B, C or D, B, E

Must have commas!Otherwise you are naming a plane.

Ray – has a definite starting point and extends without end in one

direction.

The starting point of a ray is called the endpoint.

A ray is named using the endpoint first, then another point on the ray.

DF CA

*Naming a ray: arrow always points right!

Ray cont…

Look at the pairs of rays

MP MQ

PM MP

PM PQ

MN PQ

Line Segment – a part of a line consisting of 2

endpoints and all points betweenName using its endpoints

MN NM

PQ

MQ

Example

Name 2 segments and one ray.

BDPB&

Don’t name the same thing twice unless it asked for the different ways of naming.

Sample answers:

PCWhy does ray BD not work?

Plane – a flat surface that extends without end in

all directions For any 3 noncollinear points, there is only one plane that contains all 3 points.

A plane can be named with a single uppercase script letter or by three noncollinear points.

Plane named: ABC or M

Definitions

Coplanar – Points that lie in the same plane

Noncoplanar – Points that do not lie in the same plane.

Hands-On ActivityPlace points B, C, D, E near the corners of a piece of paper.

Place point A in the middle of the paper

Fold the paper so that point A is on the crease.

Open the paper slightly. The two sections of the paper represent different planes. Name 3 points that are coplanarName 3 points that are noncoplanarName a point that is in both planes

A, E, D

D, A, C

A