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# Unit 11 Proofs

### Deck of vocab and theorems used in proofs

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