algebraic and geometric proofs

Definition of Congruent Segments

If AB ≅ CD, then AB = CD

Definition of Congruent Angles

If ∠2 ≅ ∠3, then m∠2 = m∠3

Segment Addition Postulate

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

Definition of Midpoint

If M is the midpoint of XY, then XM ≅ MY

Definition of a Right Angle

If ∠A is a right angle, then m∠A = 900

Angle Addition Postulate

If D is in the interior of ∠ABC, then

Definition of Angle Bisector

If YW bisects ∠XYZ, then ∠XYW ≅ ∠ZYW

Definition of Complementary Angles

If 2 angle measures have a sum of 900, then the angles are complementary

Definition of Supplementary Angles

If 2 angle measures have a sum of 180,

then the angles are supplementary

Linear Pair Theorem

If ∠1 and ∠2 form a linear pair,

then ∠1 and ∠2 are supplementary

Vertical Angles Theorem

If ∠A and ∠B are vertical angles, then

∠A ≅ ∠B

Congruent Complements Theorem

If ∠1 and ∠2 and are complementary &

∠2 & ∠3 are complementary, then ∠1 ≅ ∠3

Congruent Supplements Theorem

If ∠1 and ∠2 and are supplementary &

∠2 & ∠3 are supplementary, then ∠1 ≅ ∠3

Right Angle Congruence Theorem

If ∠A and ∠B are right angles, then

∠A ≅ ∠B

Addition Property of Equality

If a = b, then a + b = 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 = , c ≠ 0

Reflexive Property of Equality

a = a

Substitution Property of Equality

if a = b, then b can be substituted for

a in any expression

Symmetric Property of Equality

If a = b, then b = a

Transitive Property of Equality

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

Distributive Property

a(b + c) = ab + ac

Simplify

Combine Like Terms