Definitions
Midpoint
a point that divides a segment into 2 CONGRUENT segments
Vertical Angles Theorem
If two angles are vertical then they are CONGRUENT
Segment Addition Postulate
If C is between A and B then AC + BC = AB
Symmetric Property
a=b then b=a
Law of Detachment
if "p" then "q"
"p"
therefore "q"
Segment Bisector
a point, line, segment, or ray that intersects a segment at the midpoint.
Right Angle Congruence Theorem
All right angles are congruent
Angle Addition Postulate
m<ABC +m<CBD =m<ABD
two parts of one angle add up to the whole angle.
Transitive Property
Law of Syllogism
If "p" then "q"
If "q" then "r"
therefore If "p" then "r"
Vertical Angles
2 angles whose sides form opposite rays
Congruent Supplements Theorem
If two angles are supplementary to the same angle then they are congruent
Linear Pair Postulate
if two angles form a linear pair then they are supplementary
Addition Property of Equality
if a=b then a+c=b+c
Law of Contrapositive
If "p" then "q"
~ q
therefore ~ p
Complementary Angles
2 angles that sum to 90 degrees
Congruent Complements Theorem
If two angles are complementary to the same angle then the two angles are congruent
Linear Pair
2 angles that are adjacent and supplementary
Property of Congruence
congruent segments are equal in length.
congruent angles are equal in degree.
Equivalence Statements
Statements with the same truth value
i.e.
Conditional - Contrapositive
Converse - Inverse
Supplementary Angles
2 angles that sum to 180 degrees
Angle Bisector
a ray that divides an angle into 2 congruent angles
Biconditional Statement
a logical statement that is written as p if and only if q
both conditional and converse must be true.