geometry vocab

congruent supplements theorem

if two angles are supplementary to the same angle, then they are congruent

congruent complements theorem

if two angles are complementary to each other, then they are congruent

linear pair postulate

if two angles form a linear pair, then their measures sum up to 180 degrees

vertical angles theorem

if two angles are pairs of vertical angles, then they are congruent

conditional statement

a logical statement that has a hypothesis and conclusion

if-then form

a conditional statement in the form “if p, then q” where the “if’ part contains the hypothesis and the “then” part contains the conclusion

hypothesis

the “if” part of a conditional statement written in if-then form

conclusion

the “then” part of a conditional statement written in if-then form

negation

the opposite of a statement

converse

the statement formed by exchanging the hypothesis and conclusion of a conditional statement

inverse

the statement formed by negating both the hypothesis and conclusion of a conditional statement

contrapositive

the statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement

equivalent statement

two related conditional statements that are both true or both false

perpendicular lines

two lines that intersect to form a right angle

biconditional statement

a statement that contains the phrase “if and only if”

truth value

a value that represents whether a statement is true or false

truth table

a table that shows the truth values for a hypothesis, conclusion, and a conditional statement

conjecture

an unproven statement that is based on observations

inductive reasoning

process of forming hypotheses based on observed patterns or examples

counterexample

a specific case for which a conjecture is false

deductive reasoning

a process that uses facts, definitions, accepted properties, and the laws of logic to form a logical argument

line perpendicular to a plane

a line that intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point

proof

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

two-column proof

a type of proof that has numbered statements and corresponding reasons that show an argument in a logical order

theorem

a statement that can be proven

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 a x c = b x c

division property of equality

if a =b, then a/c=b/c, c does not equal 0

substitution property of equality

if a =b, then a can be substituted for b (or b for a) in any equation or expression

distributive property

sum: a(b+c) = ab+ac

difference: a(b-c)= ab-ac