# Postulates

## 22 terms

### Theorem

A mathematical statement or proposition that is derived from previously accepted results. Theorems are based on postulates, definitions, or on other established theorems.

### Corollary

A theorem that follows easily from another theorem that has already been proved

### Perpendicular Line Postulate

Through a point outside a line, there is exactly one line perpendicular to the given line

### Point at midpoint postulate

A segment has exactly one midpoint

### Point at intersection postulate

Two lines intersect in exactly one point

### Parallel Line postulate

Through a point outside a line, there is exactly one line parallel to the given line

### Angle bisector postulate

An angles has exactly one bisector

If B is between A and C, then AB + BC = AC

The measures of the angles formed by two adjacent angles is the sum of the measures of these two angles

### Perpendicular postulate

The perpendicular segment from a point to a line is the shortest segment from the point to the line

If a = b and c = d, then a + c = b +d

### Subtraction property of equality

If a = b and c = d then a - c = b - d

### Multiplication property of equality

If a = b then ca = cb

### Division property of equality

If a = b and c does not equal 0 than a/c = b/c

### Substitution property of equality

If a = b then either a or b may be substituted for other in any equation

a = a

### Transitive property of equality

If a = b and b =c then a = c

a + b = b + a

ab = ba