Geometry unit 2 (proofs)

Conjecture

The statement of an observation

Counterexample

An example that shows a conjecture to be false

Conditional statement

A statement written in a if-then form including a hypothesis (if) and a conclusion (then)

Inverse conditional

Adding not to the hypothesis and conclusion (if not p, then not q)

Converse conditionals

Switching the hypothesis and conclusion (q to p)

Contrapositive conditionals

Converse and inverse (using not statements and switching the hypothesis and conclusion)

Bi conditional statements

Statement that makes both converse and regular conditional statements true

Disjunction conditionals

Statements using or (the statement is true only when at least one of the statements is true

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

If a=b, then a・c=b・c

Division property

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

Distributive property

If a(b+c), then it equals to ab+ac

Substitution property

If a=b, then a can be replaced by b in an equation/statement

Reflexive property

(Any real number) a=a

Symmetric property

If a=b, then b=a

Transitive property

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

Reflexive property of congruence

(For any segment) with line on top AB~=~AB

Symmetric property of congruence

If AB=CD (congruent) then CD=AB (congruent)

Transitive property of congruence

If AB=CD (congruent) and CD=XY (congruent), then AB=XY

Definition of Congruence

If AB=CD (congruent) with the same measure, then it’s equal to AB=CD (measure)

Definition of midpoint

AM=MB (both congruent and measure) if M is the midpoint of AB

Segment Addition Postulate

AB+BC=AC if all points are Collinear and b is in between a and c

Definition of Angle bisector

An angle bisector divides an angle into two equal parts

Definition of complementary angles

The sum of the angles are 90 degrees

Definition of supplementary angles

The sum of the angles are 180 degrees

Definition of perpendicular

Lines forming a 90 degree angle

Definition of a right angle

90 degree angle

Angle addition postulate

ABD+DBC=ABC

Vertical angles theorem

If two angles are vertical, they are congruent

Complement theorem

If two angles form a right angle, they are complementary

Supplement theorem

If two angles form a linear pair, they are supplementary

Congruent complements theorem

If A is complementary to B and C is complementary to B, then A=C (congruent)

Congruent Supplements theorem

If A is supplementary to B and C is supplementary to B, then A=C (congruent)