Everything for proofs

Linear pair postulate

If two angles form a linear pair then they are supplementary

Vertical angles congruence theorem

Vertical angles are congruent

Congruent complements theorem

If two angles are complementary to the same angle then they are congruent/equal

Congruent supplements theorem

If two angles are supplementary to the same angle then they are congruent

Right angles congruence theorem

All right angles are congruent

Addition property of equality

If a=b then a+c=b+c

Subtraction property of equality

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

multiplication property of equality

If a=b then axc=bxc

Division property of equality

If a=b then a/c=b/c when c does not equal 0

substitution property of equality

If a=b then a can be substituted for b in any equation or expression

distributive property of equality

If a(b+c)=ab+ac and a(b-c)= ab-ac

Reflexive property of line/angle congruence

AB=AB Something equals itself

transitive property of equality

If AB=CD and CD=EF then AB=EF

The definition of segment/angle congruence

congruent segments/angles have the same length/measure

The definition of segment/angle bisector

divides a segment/angle into two congruent parts

The definition of the midpoint of a segment

A point that divides a segment into two congruent parts

The definition of perpendicular lines

two lines that intersect while making 90 degree angles

The definition of linear pairs

2 adjacent formed by intersecting lines

The definition of vertical angles

2 non-adjacent formed by intersecting lines

The definition of supplementary angles

two angles with the sum of 180 degrees

The definition of complementary angles

two angles with the sum of 90 degrees

The definition of right angles

Angles with the measure of 90 degrees

The definition of bisect

To divide into two congruent parts

Conditional statement

A statement that contains a hypothesis and conclusion. Most commonly put into if-then form

Converse

The hypothesis and conclusion are swapped from the conditional statement

inverse

The negation of both the hypothesis and conclusion of a conditional statement

Contrapositive

The reverse and negation of a conditional statement

Biconditional

conditional statement with “if and only if” instead of “if” this must work backwards as well

Symbol of Biconditional

P↔Q

Negation

The opposite of a statement

Conjecture

An unproven statement based on observation (Not a Conditional statement)

Inductive reasoning

The process of looking for patterns to form a conjecture

deductive reasoning

A process that uses definitions, laws of logic and facts to form a logical statement

Counter example

A specific case where a conjecture is false

Law of syllogism

A statement that links more than one conditional statement, to form a new conclusion from two existing ones (similar to the transitive property)

Law of detachment

If the hypothesis of a true conditional statement then the conditional statement is also true

The definition of a proof

A logical statement that uses deductive reasoning to show that a statement is true

Theorem

A statement that can be proven

Postulate

A statement that is accepted as true

Symmetric prop. of angle/segment congruence

If AB≅CD then CD≅AB The equation flipped over the ≅

Transitive property of segment/angle congruence

m<A≅m<B and m<B≅m<C so m<A=m<C

Line-point postulate

A line contains at least 2 points

Two point postulate

Through any two points there exists a line

Line intersection postulate

If two lines intersect, then their intersection is a point

Three point postulate

Through any here noncollinear points there exists a plane

Plane-point postulate

A plane contains at least three noncollinear points

Plane-line postulate

If two points lie on a plane, then the line containing them lies in a plane

Plane intersection postulate

If two planes intersect, their intersection is a line

Symmetric property of equality

AB=BC then BC=AB