Chap. 2 Math Terms

Law of Detachment

If P --> Q is true, and P is true, then Q is also true

Law of Syllogism

If P --> Q is true, and Q -->R is true, then P --> R is true also

conjunction; ^

compound statement joined by "and" where all statements must be true in order to be true

disjunction

compound statement joined by "or" where all statements have to be false for it to be false

biconditional

conjunction of two statements consisting of a conditional and its converse; false if either the conditional or converse is false

conditional statement

if-then statement, if there are no counter-examples, it is true; P --> Q

hypothesis

phrase immediately following if

conclusion

phrase immediately following then

Right angle theroems

* Perpendicular lines intersect to form four right angles * all right angles are congruent * perpendicular lines form congruent, adjacent angles * if 2 angles are congruent and supplementary, they are right angles * if 2 angles form a linear pair, then they are right angles

Properties of an Equality

* substitution: plug in a variable * reflexive: a=a * symmetric: if a=b, then b=a * transitive: if a=b and b=c, then a=c * addition: if a=b, then a+c = b+c * subtraction: if a=b, then a-c=b-c * multiplication: if a=b, then a * c = b * c * division: if c does not equal zero, then a/c=b/c * distributive: a(b+c)= ab + ac

Postulates (on the justification sheet also

* through any two points there is exactly one line * through any three noncollinear points, there is exactly one plane * A line contains at least two points * a plane contains at least three noncollinear points * if two points like in a plane, then the entire line containing those points lies in that pane * if two lines intersect, then that intersection is a point * if two planes intersect, then their intersection is a line * segment addition postulate * ange addition postulate

steps to writing a proof

1. Rewrite in if -then form 2. Draw - and label a pic according to the if -then statement 3. State - given= hypothesis of conjecture prove= conc. of conjecture (use labels) 4. Plan - in ur head or in discussion 5. Prove - write proof

compound statement

2 or more statements joined by "and" or "or"

Segment Addition Postulate

If a point B lies on a line segment AC, then AB + BC = AC the measure of a line is the sum of the two segments that make it up

Complement Theorem

If the non common sides of 2 adjacent angles form a right angle, then the angles are complementary

Mdpt Theorem

The coordinates of the midpoint of a line segment are the average of the coordinates of its endpoints.

Overlapping Segments Theorem

You are given that AB = CD. Add BC to both sides of the equation, resulting in AB + BC = BC + CD with the Addition prop of equality. AB + BC = AC and BC + CD = BD by the Segment Addition Postulate. use substitution that AC = BD

Which pairs will always have the same truth value

a conditional and a contrapositive, an inverse and a converse

counter-examples

a conjecture based on several observations, it takes one counter-example to show that a conjecture is untrue

inductive reasoning

a pattern of examples or observation to make a conjecture

theorem

a statement or conjecture that has been proven, and it can b used as reason to justify statements in other proofs

conjecture

an educated guess based on known information

Congruent Complements Theorem

angles complementary to the same angle or to congruent angles are congruent

Congruent Supplements Theorem

angles supplementary to the same angle or to congruent angles are congruent

proof

argument to arrive at a conclusion about a geometric statement

converse statement

exchanging the hypothesis and conclusion of the conditional; Q --> P

deductive reasoning

facts, rules, laws, to explain why something is true

Truth Value: Biconditional

false if any part is false

Truth Value: Conjunction

false if any part is false

Vertical Angles Theorem

if 2 angles are vertical angles, then they are congruent

Angle Addition Postulate

if B is in the interior of AOC, then AOB + BOC = AOC the measure of an angle is the sum of the two smaller angels inside

Supplement Theorem

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

inverse statement

negating both the hypothesis and conclusion of the conditional; ~P --> ~Q

contrapostive statement

negating both the hypothesis and conclusion of the converse statement; ~Q --> ~P

Truth Value: Disjunction

only false if every part is false

Truth Value: Conditionals

only false when it goes T --> F

the negation; ~

opposite of the original statement

postulate (axiom)

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

logically equivalent

statements with the same truth value

truth value

whether the statement is true