Math ch.2

conjecture

conclusion

counterexample

proving something is false

statement

if p then q

truth value

determining true or false

negation

taking the opposite (~)

compound statement

2 statements combined with “and” / “or”

conjunction

“and” both parts must be true (∧)

disjunction

“or” only one part has to be true “V”

hypothesis

if …

conclusion

then …

converse

switch the p and q

inverse

negate (opp.) both p and q

contrapositive

flip p and q then negate both

Law of Detachment

If p then q, because p is true therefore q is also.

Law of Syllogism

If p then q, if q then r, therefore p then r (conclusion)

postulate

a fact that doesn’t need to be proved

theorem

A statement that can be proved (usually if, then)

segment addition

part + part = whole segment

rst 123

reflexive, symmetric, transitive

reflexive

anything is equal to itself ex. 23x=23x (usually 1 equal sign)

symmetric

mirror image ex. if x=7, then 7=x (usually 2 equal signs)

transitive

if a=b, b=c, then a=c (usually 3 equal signs)

substitution

simplify equation ex. if 5-5+x=10-7, then x=3

2.1

through any 2 points, there’s exactly one line (2 pts. 1 line)

2.2

through any three points not on the same line, there’s exactly one plane (3 noncollinear pts. 1 line)

2.3

a line contains at least 2 points

2.4

if 2 points lie in a plane, then the entire line containing those points lies in that plane. (2 pts. on one plane, entire line on that plane)

2.5

if 2 points intersect, then their intersection is exactly one point (intersection is 1 pt)

2.6

it two planes intersect, then their intersection is a line (2 planes intersection is line)