Why do chairs sometimes wobble?Have you ever noticed that a four

legged chair sometimes wobbles, but a three- legged stool never wobbles?

Points, Lines and PlanesSection 1.12

Points An undefined term in geometry. (explained using

examples and descriptions.) They have no size How do you represent a point?

By using a dot How do you label a Point?

With a capital letter Never use the same letter on two different points. A point has neither shape nor size. What are some examples of points?

Stars, Corner of the room

HAS NO LENGTH ,WIDTH, or AREA!

A

B

BXC

Draw points and label on vocabulary sheet. 

Lines A basic undefined term of

geometry. A line is made up of points and has no thickness or width.

In a figure, a line is shown with an arrowhead at each end.

Lines are usually named by lowercase script letters or by writing capital letters for two points on the line, with a double arrow over the pair of letters.

Draw and label lines on vocabulary sheet.

Examples of lines:Phone lines strung between poles,

spider webs, sun beams.Collinear Points: (draw on vocab

sheet)Points that lie on the same line.

Non-collinear Points:(add to vocab sheet)Points that do not fall on the same line.

PlanesUndefined term in geometryAre thought of as flat surfaces that extend

indefinitely in all directions and have no thickness.

There are two ways to label planes:1. Using a capital script letter – S2. Using any three non-collinear points –

XYZ, XZY, YXZ, YZX, ZXY, ZYX Two planes intersect in one line.

Draw and label planes on vocabulary sheet.

Planes are unbounded flat surfaces with no edges or corners.

Coplanar:Points that lie on the same

plane.

Non-coplanar: (add to vocabulary sheet)

Points that do not lie on the same line.

What are some examples of planes in the classroom?Top of deskWallChalkboard

Remember: A plane extends indefinitely in all directions. The examples above do not completely satisfy the description.

Activity1. Each student gets two cards2. Label one Q and one R.3. Hold the two card together and place

a slit halfway through both cards.4. Hold cards so that the slits matchup

and slide them together. (Tape cards together)

5. Where the cards meet models a line. Draw the line and label two points C and D on the line.

Activity Cont.

1. Draw point F on your model so that it lies in Q but not R. Can F lie on line DC?

2. Draw point G so that is lies in R but not Q. Can G lie on line DC?

3. If point H lies in both Q and R where would it lie? Draw it on your model.

4. Draw a sketch of your model on your paper. Label each part appropriately.

102nd floor

82nd floor

Which tennis balls are coplanar?

Example 1: Use the figure to name each of the following.

1. Give two other names for .2. Give two other names for Plane R.3. Name 3 collinear points.4. Name 4 points that are coplanar.5. Name a point that is not coplanar with points

Q,S,and T.

V

R

Q

SP

Tm

n

PQ

Example 2: Draw and label a figure for each relationship.

RA

P

E

B

D

C

Space

Is a boundless three dimensional set of all points. Space can contain lines and planes.

1. How many Planes are there?2. Name three points that are

collinear.3. Are points A, B, C, & D coplanar?

Explain.4. At what point do and

intersect?

AB CD

Example 3

1. How any planes are there?2. Name three collinear points.3. Are points G, A, B, & F coplanar?

Explain4. At what point do and

intersect?

EF AB

Example 4

As you look at the cube, the front face is on which plane?

The back face is on which plane?

The left face is on which plane?

The back and left faces of the cube intersect at?

Planes HGC and AED intersect vertically at?

What is the intersection of plane HGC and plane AED?

Example 5Points, Lines, and Planes

.

Example 6Name each shaded plane

1-2

Line Segment

A measurable part of a line that consists of two points, called endpoints, and all of the points between them.

Ray

It has one endpoint and extends indefinitely in one direction. is a ray if it is the set of points consisting of and all points S for which Q is between P and S

Opposite RayTwo rays that share the same endpoint and form a line

1. Name three collinear points.

2. Name two different planes that contain points C and G.

3. Name the intersection of plane AED and plane HEG.

4. How many planes contain the points A, F, and H?

5. Show that this conjecture is false by finding one counterexample: Two planes always intersect in exactly one line.

Use the diagram at right.

D, J, and H

planes BCGF and CGHD

HE

1

Sample: Planes AEHD and BFGC never intersect.

Example 7Points, Lines, and Planes

Points X, Y, and Z are the vertices of one of the four triangular faces of the pyramid. To shade the plane, shade the interior of the triangle formed by X, Y, and Z.

Shade the plane that contains X, Y, and Z.

Example 8Points, Lines, and Planes

Why do chairs sometimes wobble?Have you ever noticed that a four

legged chair sometimes wobbles, but a three legged stool never wobbles? This is an example of points and how they lie in a plane. Explain.