1.2 Points, Lines, & Planes1.2 Points, Lines, & Planes

p. 10p. 10

What is a definition?What is a definition?

• Known words used to describe a new Known words used to describe a new wordword

Undefined termsUndefined terms – not formally defined – not formally defined

There are 3 in geometry.There are 3 in geometry.

PointPoint LineLine PlanePlane

PointPoint

1. Has no dimension (no length, width, 1. Has no dimension (no length, width, thickness)thickness)

2. Usually represented by a dot2. Usually represented by a dot

3. Named using one capital letter3. Named using one capital letter

• BB

LineLine1.1. Extends forever in one dimension (length)Extends forever in one dimension (length)

2.2. Has an arrowhead on each end Has an arrowhead on each end representing the fact that it goes on representing the fact that it goes on foreverforever

3.3. Consists of an infinite amount of pointsConsists of an infinite amount of points

4.4. Always straightAlways straight

5.5. Named with a lowercase script letter or by Named with a lowercase script letter or by 2 points on the line2 points on the line

AA BB

ll

Can be called:Can be called:

Line Line ll

Line AB or ABLine AB or AB

Line BA or BALine BA or BA

PlanePlane

1.1. Extends forever in 2 dimensions (length & Extends forever in 2 dimensions (length & width)width)

2.2. A flat surface consisting of infinitely many A flat surface consisting of infinitely many pointspoints

3.3. Usually represented by a 4-sided figureUsually represented by a 4-sided figure

4.4. Named with a capital script letter or 3 Named with a capital script letter or 3 points on the surface of the planepoints on the surface of the plane

AA

BC

W Can be named:Can be named:

Plane Plane WW

Plane ABC, plane BCA, plane Plane ABC, plane BCA, plane CBA, etc.CBA, etc.

More DefinitionsMore Definitions

• Collinear points –Collinear points –

points that lie on the same points that lie on the same lineline

• Coplanar points – Coplanar points –

points that lie on the same planepoints that lie on the same plane

Turn to page 10 in your book; look at Turn to page 10 in your book; look at example #1.example #1.

Line SegmentLine Segment (or segment) (or segment)

• A section of a line that has 2 endpointsA section of a line that has 2 endpoints

• Named by its endpoints. AB or BANamed by its endpoints. AB or BA

AA BB

RayRay• Piece of a line with only one endpoint Piece of a line with only one endpoint

(initial point) and continues forever in the (initial point) and continues forever in the other directionother direction

• Named by the endpoint and a second point Named by the endpoint and a second point named on the ray. (name MUST begin with named on the ray. (name MUST begin with the endpoint!)the endpoint!)

ABAB

AABB

Opposite RaysOpposite Rays

• 2 rays that share a common initial point 2 rays that share a common initial point and face opposite directions. and face opposite directions.

• QP and QS are opposite rays.QP and QS are opposite rays.

PP QQ SS

ExampleExample: 6 volunteers please!: 6 volunteers please!

• Draw & label points A & B.Draw & label points A & B.

• Draw & label points C & D.Draw & label points C & D.

• Draw AB.Draw AB.

• Draw BC.Draw BC.

• Draw AC.Draw AC.

• Draw DA.Draw DA.

More DefinitionsMore Definitions• IntersectIntersect – –

2 or more figures intersect if they 2 or more figures intersect if they have one or more points in have one or more points in

common.common.• IntersectionIntersection – –

all points or sets of points the all points or sets of points the figures have in commonfigures have in common

• What is the intersection of:What is the intersection of:

AB & DAAB & DA

BC & ACBC & AC

BC & BCBC & BC

When 2 planes intersect, When 2 planes intersect, their intersection is a line.their intersection is a line.

Assignment