Geometry- Postulates

26 terms

If two planes intersect, then their intersection ___________________________.

is exactly one line.

Line Postulate

Through any two points there exists exactly one line. (Two points determine exactly one line.)

Plane Postulate

Through any three noncollinear points there exists exactly one plane. (Three noncollinear points determine exactly one plane.)

Flatness (Flat Plane) Postulate

If two points of a line lie on a plane, then the whole line lies on the plane.

Distance Postulate

To each set of two points there is a unique positive number called the distance between the two points

Ruler Postulate

Given a line and the set of reals there is a one-to-one correspondence between the set of reals and the points on the line such that: if the coordinates of the points are a and b, then AB equals the absolute value of a minus b equals the absolute value of b minus a

If R,P, and Q are three points on a line and R is a point between points P and Q, then PR plus RQ equals PQ

Betweenness Postulate

If R,P, and Q are three collinear points and PR plus RQ equals PQ, then R lies between P and Q

Angle Measurement Postulate

To each angle there corresponds a unique, positive number between zero degrees and one eighty degrees called its measure

Protractor Postulate

given angle ACB and the coordinate of ray CA is "a" and the coordinate of ray CB is "b" then the measure of angle ACB equals the absolute value of a minus b

Angle Construction Postulate

Given a ray AB and one halfplane formed by line AB and a number x such that zero degrees is less than x is less than one eighty degrees, then there exists exactly one ray AC such that the measure of angle BAC equals x.

If S is a point in the interior of angle PQR, then the measure of angle PQS plus the measure of angle SQR equals the measure of angle PQR

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary

Every plane contains_________________________.

at least three noncollinear points

one plane

Space Postulate

Space contains at least four noncoplanar points

Plane Separation Postulate

Given a line and a plane containing it, the points of the plane not on the line form two nonempty, disjoint sets such that: 1)each set is convex and is called a halfplane 2)if P is in one halfplane and Q is in the other, then segment PQ intersects the given line or edge

Space Separation Postulate

Given space, the points of space that do not lie on a given plane form two nonempty, disjoint sets such that: 1)each set is convex and is called a halfspace 2)if P is in one halfspace and Q is in the other, then segment PQ intersects the given plane or face

Side Angle Side Postulate

Given a correspondence between triangles such that two pairs of corresponding sides are congruent and their included angles are congruent, then the triangles are congruent

PCA

If two parallel lines are CBT, then each pair of corresponding angles is congruent.

Parallel Postulate

Given a line and a point not on it, then there is exactly one line through the point parallel to the given line in the given plane.

Area Postulate

To each polygonal region there corresponds a unique positive number called its area.

If a region R is composed of two non-overlapping regions, then R equals Region one union Region two and the area of R equals the area of Region one plus the area of Region two.

Congruence Postulate

If two triangles are congruent, then their regions have the same area.

Unit Postulate

The area of square region is side times side or the area of square region is side squared.