# math postulates,theorems, and properties

## 33 terms

if point B is in the interior of <AOC the m<AOB + m<BOC = m<AOC.

### Corresponding Angles Postualte

If a transveral intersects two parallel lines then corresponding angles are congruent.

### Converse of the Corresponding Angles postulate

If two lines and a transveral form corresponding angles that are congruent then the two lines are parallel.

If a=b the a+c = b+c

### Subtraction Property of Equality

If a=b then a-c = b-c

### Multiplication Property of Equality

If a=b then a X c = b X c

### Division Property of Equality

If a=b then a/c = b/c

### Reflexive Property of Equality

A=A (everything is equal to itself)

If a=b then b=a

### Transitive Property of Equality

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

### Substitution Property of Equality

If a=b then b can replace a in any expression.

### The Distributive Property

a(b+c) = a X b + b X c

AB =~ AB
<A =~ A

### Symmetric Property of Congruence

AB =~ CD then CD =~ AB
<A =~ <B then <B =~ <A

### Transitive Property of Congruence

If <A =~ <B and <B =~ <C then <A =~ <C

### Vertical Angles Theorem

Vertical angles are congruent.

### Congruent Supplements Theorem

If two angles are supplementary of the same angle (or congruent angles) then the angles are congruent.

### Congruent Complements Theorem

If two angles are complements of the same angle (or congruent angles) thn the two angles are congruent.

### Theorem 2-4 (right angles)

All right angles are congruent.

### Theorem 2-5

If two angles are congruent and supplementary then each is a right angle.

### Alternate Interior Angles Theorem

If a transversal intersects two parallel lines then alternate interior angles are congruent.

### Same Side Interior Angles Theorem

If a transversal intersects two parallel lines 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 Angles Theorem

If a transversal intersects two parallel liknes then same side exterior angles are congruent.

### Converse of Alternate Interior Angles Theorem

If two lines and a transversal form alternate exterior angles that are congruent then the two lines are parallel.

### Converse of the same Side Interior Angles Theorem

If two lines and a transversal form same side interior angles that are supplementary the two lines are parallel.

### Converse of Alternate Exterior Angles Theorem

If two lines and a transversal for alternate exterior angles that are congruent then the lines are parallel.

### Converse of the same side exterior Angles Theorem

If two lines and a transveral form same side exterior angles that are supplementary the lines are parallel.

### Theorem 3-9

If two lines are parallel to the same line then they are parallel to eachother.

### Theorem 3-10

In a plane if two lines are perpendicular to the same line then they are parallel to eachother.

### Theorem 3-11

In a plane if a line is perpendicular to one of two parallel lines then it is perpendicular to the other.

### Triangle Angle Angle Sum theorem

The sum of the measures of the angles of a triangle is 180.

### Triangle Exterior angle Theorem

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