Geometry Unit 3 Flashcards
inductive reasoning
making a conclusion based on observations and patterns
conjecture
a concluding statement reached using inductive reasoning
a statement is ___
a sentence that is either true or false
negation
opposite truth value (~)
conjunction
statements joined by and written as P ^ Q
disjunction
statement joined by the word or written as P V Q
for a conjunction, how many statements have to be true for it all to be true?
both
for a disjunction, how many statements have to be true for it all to be true?
one
inverse
negate the hypo. and conc.(~p->~q)
converse
switch the hypo. and concl. (q->p)
contrapositive
negate and switch the hypo and conc. (~q->~p)
biconditional stataments
conjunction of the conditional and its converse
for biconditionals, how many statements have to be true for it all to be true?
both
deductive reasoning
reasoning logically & drawing a concl. from given facts and statements
law of detatchment
given a conditional, if the hypoth. is true, the concl. is true
law of syllogism
allows u to draw a concl. from 2 conditional statements where the conc. of the 1st is the hypo. of the 2nd.
substitution property
if a=b then a may be replaced by b in any equation.
symmetric prop.
if a=b then b=a
transitive property
if a=b, and b=c, then a=c
what can be used as reasons?
properties, definitions, postulates, and theorems
reflexive property of congruence
For any segment AB, ss AB ≅ ss AB
symmetric property of congruence
if ss AB ≅ ss CD, then ss CD ≅ ss AB
def of congruence
the measure of 2 angles are equal if and only if the angles are congruent
m∠A = m∠B ↔ ∠A ≅ ∠B
Can also be with segments
reflexive property of congruence
if ss AB ≅ ss CD, and ss CD ≅ ss EF,
then ss AB ≅ ss EF
def of MP
if M is the MP of ss AB, then AM=MB
seg. add. postulate
AB+BC=AC
def of right angle
sn angle measures 90* if and only if it is a right angle
def of compl. angles
2 angles are compl. if and only if the sum of their measures is 90*
def. of supll. angles
2 angles are suppl. if and only if the sum of their measures is 180*
def of perpendicular
perp. lines from right angles
vertical angles theorem
if 2 angles are vertical, then they are congruent.
complement theorem
if 2 angles form a right angle, then they are complementary
linear pair theorem
if 2 angles form a linear pair, then they are supplementary
congruent complements theorem
if 2 angles are complementary to the same angle, then they are congruent.
congruent supplements theorem
if 2 angles supplementary to the same angle, then they are congruent.
