A statement that describes a fundamental relationship between the basic terms of geometry
The conjunction of a conditional statement and it's converse
A statement formed by joining two or more statements
In a conditional statement, the statement that immediately follows the word then
A statement that can be written in if-then form
An educated guess based on known information
A compound statement formed by joining two or more statements with the word and.
The statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement.
The statement formed by exchanging the hypothesis and conclusion of a conditional statement.
An example used to show that a given statement is not always true.
A proof formed by a group of algebraic steps used to solve a problem.
A system of reasoning that uses facts, rules, definitions, or properties to reach logical conclusions.
A compound statement formed by joining two or more statements with the word or.
a two column proof that contains statements and reasons organized in two columns
in a conditional statement, the statement that immediately follows the word if
if then statement
a compound statement of the form "if a, then b" where a and b are statements
reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction
a paragraph proof
the statement formed by negating both the hypothesis and conclusion of a conditional statement
law of detachment
if p to q is a true conditional and p is true, then q is also true
law of syllogism
if p to q and q to r are true conditionals, then p to r is also true
statements that have the same truth values
if a statement is represented by p, then not p is the _________ of the statement
an informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true.
a statement that describes a fundamental relationship between the basic terms of geometry
a logical argument in which each statement you make is supported by a statement that is accepted as true
statements such as the converse, inverse, and contrapositive that are based on a given conditional statement
any sentence that is either true or false, but not both
a statement or conjecture that can be proven true by undefined terms, definitions, and postulates
a table used as a convenient method for organizing the truth values of statements.
the truth or falsity of a statement
two column proof
a formal proof that contains statements and reasons organized in two columns
if m is the midpoint of ab, then am is congruent to mb.
for every number a, a=a
for all numbers a and b, if a=b, then b=a
for all numbers a, b, and c, if a=b+b=e, then a=c
addition and subtraction properties
for all numbers a, b, and c, if a=b, then a+c=b+c and a-c=b-c
multiplication and division properties
for all numbers a, b, and c, if a=b, then ac=bc and if c is not equal to 0, a over c =b over c
for all numbers a and b, if a =b, then a may be replaced by b in any equation/expression
for all numbers a,b, and c, a(b+c)=ab+ac
the points on any line or line segment can be paired with real numbers so that, given any two points a and b on a line, a corresponds to zero and b corresponds to a positive real number
segment addition postulate
if b is between a and c, then ab+bc=ac
given line ab and a number r between 0 and 180, there is exactly one ray with endpoint a extending on either side of line ab, such that the measure of the angle formed is r.
angle addition postulate
if r is in the interior of angle pqs, then pqr+rqs=pqs. if pqr_rqs=pqs, then r is in the interior of pqs
if two angles form a linear pair then they are supplementary angles
if the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles
vertical angles theorem
if two angles are vertical angles, then they are congruent