Mathematical Justifications

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Presentation transcript:

Mathematical Justifications Valid Mathematical Justifications Are used to support conclusions in a proof or mathematical argument. They can be… Definitions Postulates Properties Theorems

“Definition of _____________________________” Congruent:  ↔ = Bisect: bisect ↔  Midpoint: midpoint ↔  segments Supplementary: supplementary ↔ sum 180 Right angle: rt  ↔ 90

Postulates we know… Segment Addition Postulate Angle Addition Postulate  A B C D  A C B

Properties…

Linear pair  supplementary THEN IF Linear pair  supplementary 1 2  supplementary Vertical angles congruent (Vertical s  ) 1  2 Right angles congruent (rt. s  )  1 2

Reflexive Property of = Symmetric Property of =

Definition of Supplementary Angle Addition Postulate

 ↔ = Linear Pair → supplementary

Addition Property of = Bisect ↔  Vertical s → 

Solve for x. 1 2 3 4

1 2 3 4