# Geometry Postulates, Theorems, Properties, and Definitions for proofs

Ruler Postulate

distance = absolute value of difference of coordinates

If B is between A and C, then AB+BC=AC

Midpoint of a Segment

The point that divides the segment into two congruent segments

Bisector of a Segment

a line, segment, ray, or plane that intersects the segment at its midpoint

if point B lies in the interior of <AOC then m<AOB+m<BOC=m<AOC

Bisector of an Angle

the ray that divides the angle into two congruent adjacent angles

Statment

If p then q

Converse

If q then p

Counterexample

If not q then not p

Inverse

If not p then not q

Biconditional

statement that is a combination of the converse and the statement, contains "if and only if

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 then a/c=b/c

Substitution Property

If a=b, then a can be substituted for b in any equation or expression

Reflexive Property

a=a (mirror)

Symmetric Property

If a=b, then b=a

Transitive Property

If a=b and b=c, then a=c

Distributive Property

a(b+c)=ab+ac

Midpoint Theorem

if M is the midpoint of segment AB, then AM=1/2AB and MB=1/2AB

Angle Bisector Theorem

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle

Bisector of an Angle

the ray that divides the angle into two congruent adjacent angles

Complementary Angle

two angles that add up to 90 degrees

Supplementary Angle

When the sum of the measures of a pair of angles add up to 180°

Vertical Angle

either of two equal and opposite angles formed by the intersection of two straight lines

Perpendicular Lines

Two lines that intersect to form right angles