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 Lines Lines that share a point. Y Lines m and n intersect. Point Y is the point of intersection. m n

Perpendicular Lines Two lines that intersect to form a right angle. Lines r and s intersect to form a right angle. s r

Parallel Lines Lines in the same plane that do not intersect. k j Lines k an j are parallel. k || j k || j

Parallel Planes Planes that have no common points. Planes R and S are parallel. R S

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

Collinear Points that are on the same line Collinear Points that are on the same line. A B C Points A, B and C are collinear.

Non-collinear Points that are not on the same line Non-collinear Points that are not on the same line. A B C Points A, B and C are non - collinear.

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

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

Congruent Two or more figures that have the exact same size and shape. Congruent symbol

Midpoint A point that lies on the segment and is equal distance from each endpoint. A B C

Space The set of all points.

Coplanar Points Points that lie on the same plane. Points P, Q and R are coplanar. P Q R

Coplanar Lines Lines that lie on the same plane. Lines x and y are coplanar. x y

Non-Coplanar Points Points that do not lie on the same plane. Points P, Q, R and S are non-coplanar. P Q R S

Intersecting Planes Planes that share a line. Planes W and Z intersect. Line k is the line of intersection. W Z k

Postulates/Axiom s Statements that are accepted as true.

Theorems Statements that are proven to be true.

Postulate Through any 2 points there is exactly one line. A B m Line m is the only line containing both A and B

Postulate Every line contains at least two points. A B p Line p contains points A and B.

Postulate If two lines intersect, their intersection is a point. n m Lines m and n intersect at P. P

Postulate For any three noncollinear points, there is exactly one plane containing them. A B C Q 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 X Y Z

Postulate If two planes intersect, their intersection is a line. Planes W and Z intersect in line k. W Z k

Postulate If two lines intersect, then they are coplanar. m n Lines m and l lie in only one plane.

Postulate If a line and a plane intersect, their intersection is a point or a line. I t X w Y Line t intersects Plane X at I. Line w intersects Plane Y at line w.

Postulate If two points lie in a plane, then the line containing them also lies in the plane. If R and S lie in plane B, then RS lies in plane B. B R SS 

Postulate Space contains at least four noncoplanar points. Points A, B, C, and D are noncoplanar. A B D C

Postulate There is exactly one plane containing a given line and a point not on the line. Only one plane contains T and CD.  T T C D  

THE END