Geometry Postulates

Question 1

The Line Existence Postulate

Answer 1

For any pair of points, a line exists that passes through them. Moreover, that line is unique; that is, only one line passes through a given pair of points.

Question 2

The Ruler Postulate

Answer 2

Every segment has a unique positive length; and a given line l, a point P on l and a positive real r, there exists two distinct points X and Y on l, one on one side of P and the other on the other side, such that PX=PY=r.

Question 3

The Segment Addition Postulate

Answer 3

If point C lies on segment AB between points A and B, then AC+BC=AB

Question 4

The Protractor Postulate

Answer 4

Every angle has a unique measure between 0 degrees and 360 degrees, and if we’re given a ray AB and a real r between 0 and 360, there exists rays AC and AD (possibly coincident) each coterminal with AB such that the measure of angle ABC = the measure of angle ABD = r degrees.

Question 5

The Angle Addition Postulate

Answer 5

If ray BP passes through the interior of angle ABC, then the measure of angle ABP + the measure of angle PCB = the measure of angle ABD

Question 6

Reflexivity Postulate

Answer 6

For all x, x=x.

Question 7

Transitivity Postulate

Answer 7

For all x, y and z, if x=y and y=z , then x=z. Euclid’s formulation: things equal to the same thing are equal to one another.

Question 8

Substitution Postulate

Answer 8

If x=y, then in any expression or equation where x occurs, we may replace x with y.

Question 9

Addition Postulate

Answer 9

If a=b and x=y, then x+a = y+b.
Euclid’s formulation: Equals added to equals yield equals.

Question 10

Subtraction Postulate

Answer 10

If a=b and x=y, then x-a = y-b. Euclid’s formulation: Equals subtracted from equals leaves equals.

Question 11

Multiplication Postulate

Answer 11

If a=b and x=y, then ax=by.

Question 12

Division Postulate

Answer 12

If a=b, x=y and a is not equal to zero, then x/a = y/b.

Question 13

Distribution Postulate

Answer 13

For all x, y and z; x(y+z) = xy + xz

Question 14

The Law of Trichotomy (Postulate)

Answer 14

For any quantities x and y, one and only one of three possibilities obtains: x=y, x<y>y.</y>

Question 15

The Straight Angle Postulate

Answer 15

Straight angles measure 180 degrees, and angels that measure 180 degrees are straight. Equivalently: all straight angles measure 180 degrees, and only straight angles measure 180 degrees.