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Addition Property

Adding the same thing to both sides of an equation

Subtraction Property

Subtracting the same thing to both sides of an equation

Multiplication Property

Multiplying the same thiing to both sides of an equation

Division Property

Dividing the same thing on both sides of the equation

Substitution Property

If two quantities are equal, then you may replace one with the other in an expression or equation

Reflexive Property

Everything is equal to itself

Symmetric Property

Equal quantities remain equal when switched

Transitive Property

A transfer of equality. An entire side will be replaced

Distributive Property

Distributing a quantity

Converse

If q, then p.

Counterexample

An example to prove a conditional statement is false

Biconditional Statement

p if and only if q

Inverse

If not p then not q

If ¬ p then ¬ q

If ¬ p then ¬ q

Contrapositive

If not q then not p

If ¬ q then ¬ p

If ¬ q then ¬ p

Conditional

If p then q

Midpoint Theorem

If M is the midpoint of AB(line untop), then AM=1/2 AB and 1/2 AB=MB

Angle Bisector Theorem

If BX(arrow pointing >) is the bisector of Angle ABC, then mAngle ABX=1/2 mAngle ABC and mAngle XBC = 1/2 mAngle ABC

Vertical Angle Theorem

Vertical angles are congruent

Theorem 2-4

(Perpendicular Implies Congruence Theorem)

(Perpendicular Implies Congruence Theorem)

If two lines are perpendicular, then they form congruent adjacent angles

Theorem 2-5

(Congruence Implies Perpendicular Theorem)

(Congruence Implies Perpendicular Theorem)

If two lines form congruent adjacent angles, then they are perpendicular

Theorem 2-6

(Split Perpendicular Theorem)

(Split Perpendicular Theorem)

If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary

Theorem 2-7

(Supplements of Congruent Angles Theorem)

(Supplements of Congruent Angles Theorem)

If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent

Theorem 2-8

(Complements to Congruent Angles Theorem)

(Complements to Congruent Angles Theorem)

If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent

Complementary Angles

two angles whose measures have the sum of 90˚

Supplementary Angles

angles whose measures have the sum of 180˚

Vertical Angle

two angles such that the sides of one angle are opposite rays to the sides of the other angles

Perpendicular Lines

two lines that intersect to form right angles 90˚

Midpoint

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Angle Bisector

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