Points

Undefined term

No length, width, or thickness

Named with a capital letter

Lines

Undefined term -- No thickness

Length that goes on forever in two directions

A straight arrangement of points

Plane Undefined Term

Has length, width but no thickness

Extends indefinitely in all directions Plane ABC

Plane W

W

The “building blocks of geometry”:

• Ancient Greeks: “A point is that which has no part.” “A line is breadthless length”.

• Ancient Chinese: “The line is divided into parts, and that part which has no remaining part is a point.”

• Not much help, huh?

A definition is a statement that clarifies or explains the meaning of a word or phrase.• Unfortunately, we can’t define

point, line or plane w/out using words that they themselves need defining, so…

• Point, line and plane are the 3 undefined terms of geometry, yet they are the building blocks for all geometry.

• IOW, using these three words, you can define all other geometric terms/figures.

Naming Lines

Intersecting LinesIntersecting LinesLines that share a point.Lines that share a point.

Y

Lines Lines mm and and nn intersect. intersect. Point Y is the point of intersection.Point Y is the point of intersection.

m

n

Perpendicular LinesPerpendicular Lines

Two lines that intersect to form Two lines that intersect to form a right angle.a right angle.

Lines Lines rr and and ss intersect to form a intersect to form a right angle.right angle.

s

r

Parallel LinesParallel LinesLines in the same plane that do not Lines in the same plane that do not intersect.intersect.

k

j

Lines Lines kk an an j j are parallel.are parallel. kk || || jj

Skew LinesSkew Lines Lines that do not lie on the Lines that do not lie on the same plane. (They do not same plane. (They do not intersect and are not intersect and are not parallel.)parallel.)

CollinearCollinearPoints that are on the same linePoints that are on the same line.

A B C

Points A, B and C are collinear.

Non-collinearNon-collinearPoints that are not on the same Points that are not on the same lineline.

A B C

Points A, B and C are non -collinear.

Segment

AB AB

BC

Part of a line that has two endpoints and contains all of the points in between the two endpoints.

A

B

C

AB AC

Ray

CA11111111111111

BA11111111111111

A part of a line consisting of one point and all points on one side of the line from that point.

A

B

C

CB11111111111111

BC11111111111111

AC11111111111111

AB11111111111111

CongruentTwo or more figures that have the exact same size and shape.

Congruent symbol

MidpointA point that lies on the segment and is equal distance from each endpoint.

A

B

C

AB BC

Space

The set of all points.

Coplanar PointsCoplanar PointsPoints that lie on the same Points that lie on the same plane.plane.

Points P, Q and R are coplanar.Points P, Q and R are coplanar.

PQ

R

Coplanar LinesCoplanar Lines Lines that lie on the same Lines that lie on the same plane.plane.

Lines Lines x x and and yy are coplanar. are coplanar.

xy

Non-Coplanar Non-Coplanar PointsPointsPoints that do not lie on Points that do not lie on the same plane.the same plane.

Points P, Q, R and S are non-coplanar.Points P, Q, R and S are non-coplanar.

PQ

R

S

Postulates/Axioms

Statements that are accepted as true.

Theorems

Statements that are proven to be true.

Postulate

Through any 2 points there is exactly one line.

AB

mLine m is the only line containing both A and B

Postulate

Every line contains at least two points.

AB p

Line p contains points A and B.

Postulate

If two lines intersect, their intersection is a point.

nm

Lines m and n intersect at P.

P

PostulateFor any three noncollinear points, there is exactly one plane containing them.

AB

CQ

Points A, B, and C lie in Plane Q.

Postulate

Every plane contains at least three noncollinear points.

Plane A contains points X, Y and Z.

A

XY

Z

PostulateIf two planes intersect, their intersection is a line.

Planes W and Z intersect in line k.

W

Zk

Postulate

If two lines intersect, then they are coplanar.

m

n

Lines m and l lie in only one plane.

THE END