29 terms

# Geometry, Justifications

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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
Contrapositive
If not q then not 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)
If two lines are perpendicular, then they form congruent adjacent angles
Theorem 2-5
(Congruence Implies Perpendicular Theorem)
If two lines form congruent adjacent angles, then they are perpendicular
Theorem 2-6
(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)
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)
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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