# Postulates/Theorems

## 30 terms

### Postulate 1-1

Through any two points, there is exactly one line.

### Postulate 1-2

If two lines intersect, they intersect in exactly one point

### Postulate 1-3

If two plains intersect, they intersect in exactly one line.

### Postulate 1-4

Through any 3 non collinear points, there is exactly 1 plane

### Postulate 1-5 (ruler Postulate)

The points of a line can be put into a one-toone correspondence with the real numbers so that: the distance between any two points is the absolute value of the difference of the corresponding numbers

### Postulate 1-6 Segment addition postulate

If three points A,B, and C are collinear and B is between A and C, then AB+BC=AC

### Postulate 1-7

Let (ray)OA and (ray) OB be opposite rays. (ray)OA,(ray)OB, and all rays with the end point O drawn on one side of (line)AB can be prepared with real #

### Postulate 1-8 (angle addition postulate)

if point b is the interior of andgleAOC, then m<aob+m<boc=m<aoc

### Postulate 1-9

If two figures are congruent, than their areas are equal

### Postulate 1-10

The area of the region is the sum of the areas of it's non over lapping parts.

### Theorem 2-1: Vertical Angles

vertical angles are congruent

### Theorem 2-2: Congruent supplements Theorem

if two angles are supplements of the same angle or of congruent angles, then the two angles are congruent

### Theorem 2-3: Congruent complements Theorem

If two angles are complements of the same angle or of congruent angles, then the angles are congruent

### Theorem 2-4

All right angles are congruent

### Theorem 2-5

if two angles are congruent and supplementary then they are right angles

### Postulate 3-1 Corresponding angle postulate

If a transversal intersects two parallel then corresponding angles are congruent

### Theorem 3-1: Alternate interior angles Theorem

if a transversal intersects two parallel lines, then alternate interior angles are congruent

### Theorem 3-2: Same side interior angles theorem

If a transversal intersects two parallel lines, then the same-side interior angles are supplementary

### Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, the alternate exterior angles are congruent

### Same Side Exterior angle Theorem

If a transversal intersects two parallel lines, then the same side exterior are supplementary

### Postulate 3-2: Converse of the Corresponding angles postulates

If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel

### Theorem 3-5: Converse of he alternate interior angles Theorem

if two lines and a transversal form alternate interior angles that are congruent, then the two lines ae parallel

### Theorem 3-6: Converse of the same-side interior angles Theorem

if two lines and a transversal for same-side interior angles that are supplementary, then the two lines are parallel

### Theorem 3-7: Converse of Alternate exterior angles Theorem

if tow lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel

### Theorem 3-8: Converse of the same side exterior angles Theorem

if two lines and a transversal form same-side exterior angles that are supplementary, then two lines are parallel

### Theorem 3-9

if two lines are parallel to the same line, then they are parallel to the same line, then they are parallel to each other

### Theorem 3-10

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other

### Theorem 3-11

in a plane, If a line is perpendicular to one of the two parallel lines, then it is also perpendicular to the other

### Theorem 3-12: triangle Angle-sum theorem

The sum of the measure of the angles of a triangle is 180

### Theorem 3-13: triangle exterior angle Theorem

the measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles