# Geometry: Chapter 3 Terms

## 47 terms

### Axiom

A statement that describes a fundamental relationship between the basic terms of geometry

### Biconditional

The conjunction of a conditional statement and it's converse

### Compound statement

A statement formed by joining two or more statements

### Conclusion

In a conditional statement, the statement that immediately follows the word then

### Conditional statement

A statement that can be written in if-then form

### Conjecture

An educated guess based on known information

### Conjunction

A compound statement formed by joining two or more statements with the word and.

### Contrapositive

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

### Converse

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

### Counterexample

An example used to show that a given statement is not always true.

### Deductive argument

A proof formed by a group of algebraic steps used to solve a problem.

### Deductive reasoning

A system of reasoning that uses facts, rules, definitions, or properties to reach logical conclusions.

### Disjunction

A compound statement formed by joining two or more statements with the word or.

### formal proof

a two column proof that contains statements and reasons organized in two columns

### hypothesis

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

### inductive reasoning

reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction

### informal proof

a paragraph proof

### inverse

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

### logically equivalent

statements that have the same truth values

### negation

if a statement is represented by p, then not p is the _________ of the statement

### paragraph proof

an informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true.

### postulate

a statement that describes a fundamental relationship between the basic terms of geometry

### proof

a logical argument in which each statement you make is supported by a statement that is accepted as true

### related conditionals

statements such as the converse, inverse, and contrapositive that are based on a given conditional statement

### statement

any sentence that is either true or false, but not both

### theorem

a statement or conjecture that can be proven true by undefined terms, definitions, and postulates

### truth table

a table used as a convenient method for organizing the truth values of statements.

### truth value

the truth or falsity of a statement

### two column proof

a formal proof that contains statements and reasons organized in two columns

### midpoint theorem

if m is the midpoint of ab, then am is congruent to mb.

### reflexive property

for every number a, a=a

### symmetric property

for all numbers a and b, if a=b, then b=a

### transitive property

for all numbers a, b, and c, if a=b+b=e, then a=c

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

### substitution property

for all numbers a and b, if a =b, then a may be replaced by b in any equation/expression

### distributive property

for all numbers a,b, and c, a(b+c)=ab+ac

### ruler postulate

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

if b is between a and c, then ab+bc=ac

### protractor postulate

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.

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

### supplementary theorem

if two angles form a linear pair then they are supplementary angles

### complement theorem

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