Deck of vocab and theorems used in proofs
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| Addition Property of Equality | If a = b, then a + c = b + c
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| Subtraction Property of Equality | If a = b, then a – c = b – c
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| Multiplication Property of Equality | If a = b, then a • c = b • c
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| Division Property of Equality | If a = b and c ≠ 0, then a ÷ c = b ÷ c
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| Distributive Property | a (b + c) = ab + ac
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| Substitution Property | If a = b, then b may be substituted for a in any expression containing a
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| Commutative Property | a + b = b + a a • b = b • a
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| Associative Property | (a + b) + c = a + (b + c) (a • b) • c = a • (b • c)
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| Reflexive Property | a = a ∠A ≅ ∠A AB ≅ AB
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| Symmetric Property | If a = b, then b = a If ∠A ≅ ∠B, then ∠B ≅ ∠A
If AB ≅ CD, then CD ≅ AB
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| Transitive Property | If a = b and b = c, then a = c
If ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C
If AB ≅ CD and CD ≅ EF, then AB ≅ EF
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| Definition of Congruence | If two segments or angles are congruent, then they have the same length or measure. Conversely, if two segments have the same length, or two angles have the same measure, then they are congruent.
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| Definition of Right Angle | An angle that has a measure of 90˚.
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| Definition of Midpoint | The point that divides a line segment into 2 congruent segments.
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| Definition of Bisects | A ray that divides an angle into 2 congruent angles.
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| Definition of Complementary Angles | Two angles whose measures sum to 90˚.
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| Definition of Supplementary Angles | Two angles whose measures sum to 180˚.
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| Definition of Linear Pair | Two angles that share a common side and whose other sides form a straight line.
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| Definition of Vertical Angles | When two lines intersect to make an X, angles on opposite sides of the X .
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| Angle Addition Postulate | If B is in the interior of ∠AOC, then
m∠AOB + m∠BOC = m∠AOC.
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| Segment Addition Postulate | If B is a point on the segment AC, then
AB + BC = AC
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| Linear Pair Postulate | If two angles form a linear pair, then they are supplementary.
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| straight Angle Postulate | If three or more angles are arranged together to form a straight line, then they sum to equal 180˚.
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| Vertical Angle Theorem | If two angles are vertical angles, then they are congruent.
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| Same-Side Interior Angles | A pair of angles on the same side of the transversal and inside the lines
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| Alternate Interior Angles | A pair of angles on opposite sides of the transversal and inside the lines
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| Alternate Exterior Angles | A pair of angles on opposite sides of the transversal and outside the lines
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| Corresponding Angles | A pair of angles in matching positions. For example, both could be on the left side of the transversal and above the line.
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