unit 2 geometry postulates, theorems, and definitions

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≠0, then a/c=a/b

Distributive Property of Equality

a(b+c)=ab+ac, where a, b, and c are real numbers

Substitution Property of Equality

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

Simplify

make simpler (combining like terms)

Segment Addition Postulate

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

Angle Addition Postulate

if P is in the interior of ∠RST, then m∠RST=m∠RSP+m∠PST

Linear Pair Postulate

if two angles form a linear pair, then they are supplementary

Reflexive Property of Congruent Segments

for any segment AB, (line) AB≅(line) AB

Symmetric Property of Congruent Segments

If (line) AB≅(line) CD, then (line) CD≅(line) AB

Transitive Property of Congruent Segments

If (line) AB≅(line) CD and (line) CD≅(line) EF, then (line) AB≅(line) EF

Reflexive Property of Congruent Angles

for any angle A, ∠A≅∠A

Symmetric Property of Congruent Angles

if ∠A≅∠B, then ∠B≅∠A

Transitive Property of Congruent Angles

if ∠A≅∠B, and ∠B≅∠C, then ∠A≅∠C

Right Angles Congruence Theorem

all right angles are congruent

Congruent Supplements Theorem

if two angles are supplementary to the same angle (or to congruent angles), then they are congruent

Congruent Complements Theorem

if two angles are complementary to the same angle (or to congruent angles), then they are congruent

Vertical Angles Congruence Theorem

vertical angles are congruent

Definition of Supplementary Angles

the sum of two angles=180º

Definition of Complementary Angles

the sum of two angles=90º

Definition of Vertical Angles

two angles opposite each other when two lines cross, these angles are equal/congruent

Definition of Right Angles

an angle that is 90º

Definition of a Midpoint

the middle of a line segment, both sides of it are congruent/equal

Definition of Perpendicular Lines

two lines that cross each other, creating 90º angles

Definition of Congruent Segments

segments that have the same length

Definition of Congruent Angles

angles that have the same measure