geometry unit 2

converse

switch

inverse

negate both statements

contrapositive

switch and negate both

negate

switch values

^

and, both must work

^ (upside down)

or, at least one works

—>

if then, promise rule

promise rule

only false is you promise but don’t deliver (T and then F)

←->

if and only if (both need to be true)

conjunction

true only when both are true

disjunction

true when only both are false

biconditonal

true only when the truth values match

conditional

false only when T—> F

substitution property of equality

a=b, a can be substituted as b and b ca be substituted as a in any equation

addition and subtraction property of equality

add or subtract the same number from both sides of an equation

multiplication and division property of equality

multiply or divide the same number to both sides of an equation as long as the number is not 0

distributive property

multiplication can be distributed over addition and subtraction

refliexive property of equality

a=a

symmetric property of equality

if a=b then b=a

transitive property of equality

if a=b and b=c then a=c

definition of congruent segments

segment AB is congruent to segment CD if and only if AB=CD

definition of midpoint

given that M lies on segment AB then m is the midpoint of AB if and only if AM=BM

midpoint therom

if M is the midpoint of segment AB then segment AM is congruent to BM

definition of segment bisector

given that point M lies on segment AB M bisects AB only if and only if segment AM is congruent to segment BM

segment addition postulate

AB+BC=AC

definition of congruent angles

angle a is congrunt to angle b if and only if angle A is equal to angle b

definition of angle bisector

line bx bisects angle ABC if and only if angle ABX is congruent to angle CBX

angle addition postulate

if d is the interior of angle ABC then angle ABD + angle CBD = ABC

definition of complementary

angles add up to 90

definition of supplementary

angles add up to 180

vertical angles therom

if angle 1 and 2 are vertical then they are congruent

linear pair therom

if angles 1 and 2 form a linear pair then they are supplementary

polygon exterior angle theron

the sum of the measures of the exterior angles of an convex polygon is 360

polygon interior angles therom

the sum of the measures of the interior angles of a convex polygon w n sides is (n-2)x180

congruent complements theron

if 2 angles are complements of the same angles (add up to 90) then they are congruent

congruent supplements therom

if two angles are supplements (add up to 180) of the same angles then they are congruent

tautology

always true

contradiction

always false