Proofs - Im2

Addition Property of Equality

If the same number is added to equal numbers, the sums are equal.

Subtraction Property of Equality

If the same number is subtracted from equal numbers, the differences are equal.

Multiplication Property of Equality

If equal numbers are multiplied by the same number, the products are equal

Division Property of Equality

If equal numbers are divided by the same nonzero number, the quotients are equal

Reflexive property of equality

a number is equal to itself

Substitution Property

if values are equal, one value may be substituted for the other.

distributive property

an expression of the form a(b+c) is equivalent to ab+ac

addition property of equality

a = b -> a + c = b + c

subtraction property of equality

a = b -> a - c = b - c

Multiplication Property of Equality

a = b -> ac = bc

Division Property of Equality

a = b and c (=) -> a/c = b/c

Reflexive property of equality

a = a

Substitution Property

a = b -> a can be substituted for b

distributive property

a(b+c) = ab + ac

Theorem 7.1

if two angles are supplements of the same angle, then they are equal in measure

Theorem 7.2

If two angles are complements of the same angle, then they are equal in measure

Vertical angles

two angles formed by intersecting lines and facing in opposite directions

postulate 8

if the sides of an angle form a straight line, then the angle is a straight angle with measure 180 degrees

postulate 9

For any segment or angle, the measure of the whole is equal to the sum of the measures of its non-overlapping parts

Theorem 7.3

Vertical angles are equal in measure

Postulate 10

if two parallel lines are intersected by a transversal, then corresponding angles are equal in measure

Theorem 7.4

If two parallel lines are intersected by a transversal, then alternate interior angles are equal in measure

Theorem 7.5

If two parallel lines are intersected by a transversal, then co-interior angles are suplementary

Theorem 7.6

If a quadrilateral is a parallelogram then consecutive angles are supplementary

Theorem 7.7

If a quadrilateral is a parallelogram then opposite angles are equal in measure