Geometry Lesson 1.2

Points, Lines, and Planes

August 17, 2007

Objectives

� Students will be able to:

� Define: Point, line, plane, collinear, coplanar, line segment, ray, intersect, intersection

� Name collinear and coplanar points

� Draw lines, line segments, and rays with proper labeling

� Draw opposite rays

� Sketch intersections of lines and planes and two planes

Warm-Up: Common Words

�What are “common words” we use in

everyday conversation?

� Do you have to think about their

meaning?

�What if you didn’t know these words?

� In today’s lesson you will learn about

common words needed to speak the

language of geometry

Warm-Up Activity: Points & Lines� Mark the intersection of Hayden and

McDonald

� Mark the intersection of Hayden and Indian Bend

� Mark the intersection of Hayden and Jackrabbit

� What appears to be true of the dots you

made?

•Mark the intersection of

Hayden and McDonald

•Mark the intersection of

Hayden and Indian Bend

•Mark the intersection of

Hayden and Jackrabbit

•What appears to be true of

the dots you made?

1A. Points, Lines, and Planes

A location in space, but has no size or shape

AB Extends without end in

one dimension (two directions) and always

straightCalled ABor line l

AB

C

Extends without end in

two dimensions (all

directions), always flat, and has no thickness

Calledplane ABCor plane M

Called

point A

M

l

1B. Collinear and Coplanar

Points on the same line

Points

Points or Lines

Points on the same plane

D E F G

A B C

“Co” means “together”

D, E, F, and G are collinear

A, B, and C are coplanar pointsLines l and n are coplanar lines

l

n

Example 1: Naming Points

� Three points that

are collinear:

� Four points that

are coplanar:

� Three points that

are not collinear:

DE F

G

H

D, E, F

D, E, F, G and D, E, F, H (plane not shown)

H, E, G

Practice 1A: Naming Points

� Name a point that is collinear with the

given points

� B and E:

�C and H:

� D and G:

� A and C:

� H and E:

�G and B:

I

E

B

B

C

D

Practice 1B: Naming Points

� Name a point that is coplanar with the

given points

�M, N, R:

�M, N, O:

�M, T, Q:

�Q, T, R:

� T, R, S:

�Q, S, O:

T

P

P

S

Q

P

2. Line Segments and Rays

End points A and B and all

points in between

A B

A B

Line AB

Line segment AB

Starting point and all points on

one side of the starting point

A BRay AB

AB

AB

A BRay BA BA

AB

Example 2: Drawing Lines & Rays

� Draw points J, K, and L (non-collinear)

� Then, draw JK, KL, and LJ

J

K

L

Practice 2: Drawing Lines & Rays

� Draw three collinear points A, B, and C

� Draw a point D that is non-collinear with A,

B, and C

� Draw AB

� Draw BD

� Draw CD

3. Intersections

Two figures having one or

more points in common

The set of points the two figures have in

common

Lines k and l have point

A in common, so point A

is the intersection

Ak

l

(verb)

(noun)

Activity: Modeling Intersections

Activity: Questions 1-4

1. When the cards are NOT together:

What is the intersection of AB and

CD? AB and EF?

2. With the cards together, what is the

intersection of CD and EF?

3. What is the intersection of planes M

and N?

4. Are CD and EF coplanar? Explain.

Point G Point G

Point G

AB

Yes, these two intersecting lines form a plane

Closure

� Name five of the nine common words

we learned

� How far does a line go in each

direction? A plane?

� How many directions does a ray

have?

�What is it called when points are on

the same line? In the same plane?