Geometry

Lesson 1 – 1

Points, Lines, and Planes

Objective:Identify and model points, lines, and planes.

Identify intersecting lines and planes.

Undefined terms

Undefined terms: objects that are only explained using examples and descriptions.PointLinePlane

PointPoint:A point is a location.Has neither shape nor size

Named:Capital letter

ExamplePoint A

LineLine:Made up of pointsHas no thickness or widthExactly one line through and two points.

Named:Any 2 points on the line (2 capital letters)Lowercase script letter

Example line m

PQ QPor

PlanePlane:A flat surface made up of points that extends

infinitely in all directions.Exactly one plane through any 3 points not on the

same line.

NamedCapital Script letter3 points on the plane not on a line (3 capital letters)

Example

KPlane BCD (any order)

Definitions

Collinear:Points that lie on the same line

Noncollinear:Points that do not lie on the same line.

CoplanarPoints that lie in the same plane

NoncoplanarPoints that do not line in the same plane

Use the figure to name each of the following:

A line containing point W

A plane containing point X

Any one of the following work:

YXXYYWWYXWWXYV

VYXVVXWVVWnline

,,,,,,

,,,,,,

Any one of the following work: (3 letters that are noncollinear)P, plane XZY, plane VZY, plane VZW, plane WZX, plane VZX, Plane WZY

ExampleName the geometric term modeled by the objects in the picture.

Push pin

Maroon boarder

The card itself

Stripes on a sweater

Corner of a box

Point G

HJ

Sample: plane FGJ

lines

point

IntersectionIntersection of two or more geometric figures is the set of points they have in common.

Where do two lines intersect?

Where do two planes intersect?

At a point.

At a line

Draw the following

intersects plane T at point S. QR

Must have the dashed line to show that the line goes throughthe plane and is not on or in the plane.

Sample answer

Draw the following

Line p lies in plane N and contains point L.Sample answer.

Definitions

Definitions are defined terms that are explained using undefined terms and/or other defined terms.

Space: defined as a boundless, three-dimensional set of all points. Space can contain lines and planes.

How many planes appear

in this figure.

Name 3 points that are collinear.

Name the intersection of plane HDG with plane X.

At what point do LM and EF intersect? Explain.

6 planes: 5 around the pyramid and one onbottom of the the pyramid… don’t name thebottom plane twice.

Points J, K, and DMake sure you have commas otherwise it names a plane.

HG

Don’t appear to intersect since L is the only point on line LM in the plane.

Are points E, D, F,

and G coplanar?

At what point or in what line do

planes JDH, JDE, and EDF intersect?

No, not all on the same plane.

Point D is the only thing in common.

Homework

Pg. 8 1 – 12 all, 14 – 46 EOE, 52, 66 – 82 EOE