math1
Terms
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- conditional
- p -> q "If and then statement"
- converse
- reverse of conditional (q -> p)
- biconditional statement
- P if and only if Q. (p <-> q)
- law of detachment
- if a conditional is true and its hypothesis is true, then its conclusion must be true. if p -> q is a true statement and p is true, then q is true.
- law of syllogism
- if p -> q and q -> r are true statements,then p -> r.
- addition property of equality
- if a=b, then a+c=b+c
- subtraction property of equality
- if a=b, then a-c=b-c.
- multiplication property of equality
- if a=b, then ac=bc
- division property of equality
- if a=b and c does NOT=0, then a/c=b/c
- reflexive 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.
- substitution property of equality
- if a=b, then b can replace a in any expression
- distributive property of equality
- a(b+c)=ab+ac
- reflexive property of congruence
- AB~AB A~A
- symmetric property of congruence
- if AB~CD, then CD~AB if A~B, THEN B~A
- transitive property of congruence
- if AB~CD and CD~EF, then AB~EF if A~B and B~C, then A~C.
- theorem 2-1: vertical angles theorem
- vertical angles are congruent
- Theorem 2-2: congruent supplements theorem
- if 2 angles are supplements of the same angle or of congruent angles, then the 2 angles are congruent
- theorem 2-3: congruent complements theorem
- if 2 angles are complements of the same angle or of congruent angles, then the 2 angles are congruent.
- theorem 2-4
- all right angles are congruent
- vertical angles
- 2 angles whose sides are opposite rays.
- adjacent angles
- -share a common side -share a ccommon vertex -no common interior points. *angles dont have to be adjacent to be supplementary
- complementary angles
- measures add up to 90d.
- supplementary angles
- measures add up to 180d.
- postulate/axiom
- statements that we accept as true without proof
- theorem
- statements we must prove through deductive reasoning
- paragraph proof
- something explained through sentences
- 2-column proof
- shows statements and reasons in 2 columns.