Obj. 7 Algebraic Proof

1. Obj. 7 Algebraic Proof proof – an argument which uses logic, definitions, properties, and previously proven statements algebraic proof – A proof which uses algebraic properties • When you write a proof, you must give a justification (reason) for each step to show that it is valid. For each justification, you can use a definition, postulate, property, or a piece of given information.

2. Algebraic Properties Foldable • Make a hotdog fold. • Make shutters. • Open up all the folds and make a hamburger fold. • Make shutters. • Cut from the edge of the paper to the fold on each side. This should give you eight sections.

12. Example: Solve the equation 21 = 4x – 7. Write a justification for each step. 21 = 4x – 7 Given equation 21 + 7 = 4x – 7 + 7 Add. prop. = 28 = 4x Simplify 7 = x Simplify x = 7 Sym. prop. = Div. prop. =

13. Line segments with equal lengths are congruent, and angles with equal measures are also congruent. Therefore, the reflexive, symmetric, and transitive properties of equality have corresponding properties of congruence. • Hotdog fold • Open it up and hamburger fold • Make shutters • Cut one side of shutters into two sections.

14. Reflexive Property of Congruence Symmetric Property of Congruence Transitive Property of Congruence

15. fig. A  fig. A (refl. prop. ) Symmetric Property of Congruence Transitive Property of Congruence

16. Reflexive Property of Congruence If fig. A  fig. B, then fig.B  fig.A (sym. prop. ) Transitive Property of Congruence

17. Reflexive Property of Congruence Symmetric Property of Congruence If fig. A  fig. B and fig. B  fig. C, then figure A  figure C (trans. prop. )

18. Example: Write a justification for each step. Given TA = AR Def.  segments 5y+6 = 2y+21 Subst. prop. = 3y+6 = 21 Subtr. prop. = 3y = 15 Subtr. prop. = y = 5 Div. prop. = 5y+6 2y+21  T A R