Geometry Midterm

inductive reasoning

reasoning based on specific examples or past events

conjecture

unproven statement or rule based on inductive reasoning

counterex

an example that proves the conjecture false

conditional statement

an “if, then” statement that relates a hypothesis to a conclusion; p→q

biconditional statement

an “if and only if” statement where the rules work both ways

p

converse

order switch; q→p

negation

making one negative “not” \~p

inverse

same order, both negative \~p→ \~q

contrapositive

switch and negative \~q →\~p

deductive reasoning

reason using given and previously known facts

rhombus

4 equal sides, diagonals are perpendicular

rectangle

diagonals are congruent

square

4 equal sides, perpendicular and conguent diagonals

square root (x2 -x1)^2+(y2-y1)^2

distance formula

180 (n-2)

interior angle measure formula

x, x, root 2x

side values of a 45 45 right triangle

x, root 3x, 2x

side values of a 30 60 right triangle

n/360 x 2 PI r

arc length formula

n/360 x Pi r ^2

area sector formula

rhombus

diagonals are perpendicular and/or a diagonal bisects 2 angles

rectangle

diagonals are congruent

square

if the diagonals are perpendicular and congruent, and/or a diagonal bisects angles and the diagonals are congruent