geometry vocab

conjecture

an unproven statement that is based on observations

inductive resoning

looking for patterns and making conjectures

counterexample

a specific case where a conjecture is false

deductive reasoning

process that uses facts, definitions, and properties to form an argument

law of detachment

if the hypothesis of a true conditional statement is true, then the conclusion is true

law of syllogism

if hypothesis p, then conclusion q + if hypothesis q, then conclusion r = if hypothesis p, then conclusion r

conditional statement

a logical statement that has two parts, a hypothesis p and a conclusion q (if-then)

converse statement

exchange the hypothesis and the conclusion

inverse

negate both the hypothesis and the conclusion

contrapositive

first write the converse, then negate both the hypothesis and conclusion

supplementary angle

angles that form 180 degrees

complementary angle

angles that form 90 degrees

biconditional statement

when a conditional statement and its converse are both true, contains the phrase if and only if

two point postulate (2.1)

through any two points, there exists exactly one line

line-point postulate (2.2)

a line contains atleast two points

line intersection postulate (2.3)

if two lines intersect, then their intersection is exactly one point

three point postulate (2.4)

through any three noncollinear points, there exists exactly one plane

plane-point postulate (2.5)

a plane contains at least 3 noncollinear points

plane-line postulate (2.6)

if two points lie in a plane, then the line containing them lies in the plane

plane intersection postulate (2.7)

if two planes intersect, then their intersection is a line

adjacent angles

2 angles that share a common vertex and common side

linear pair

adjacent angles whose noncommon sides are opposite rays

vertical angles

2 angles whose sides form 2 pairs of opposite rays