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Algebraic Proofs

Algebraic Proofs. Warm Up Solve each equation. 1. 4 t – 7 = 8 t + 3. 2. 2( y – 5) – 20 = 0.

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Algebraic Proofs

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  1. Algebraic Proofs

  2. Warm Up Solve each equation. 1.4t – 7 = 8t + 3 2. 2(y – 5) – 20 = 0

  3. A ____proof___ is an argument that uses logic, definitions, properties and prior proven statements. Proofs are used to show that the given statement or hypothesis is true and that a conclusion can be found.

  4. The parts of a proof are: The Given (the if part of a statement) The Prove (the then part of a statement) A diagram to represent the information given. Two column chart with statements and reasons Statement Reason Always the given. The Prove Given The reasons can be postulates, theorems, properties or definition. Last step is the prove

  5. Name the property that justifies each statement: If a = b, then b = a. Symmetric Property for Equality Reflexive Property for Congruence Transitive Property for Equality If a = b and b = c, then a = c.

  6. Name the property that justifies each statement: Symmetric Property for Congruence If P  Qthen Q  P . Reflexive Property for Equality x = x If R  S and S  T then R  T . Transitive Property for Congruence

  7. Remember! Numbers are equal (=) and figures are congruent ().

  8. 2 column Algebraic Proofs practice • We will work selected problems from the book on notebook paper • Page 107 # 2 – 11

  9. Given y + 1 = 5 Sub. Prop of = –1 –1 y = 4

  10. Given 2p – 30 = -4p + 6 +4p +4p 6p – 30 = 6 Add. Prop of = +30 +30 6p = 36 Add. Prop of = 6 6 p = 6 Div. Prop of =

  11. ( ) ( ) Given 2 2 = n = Mult. Prop of =

  12. AB = BC Def. of  segments 5y + 6 = 2y + 21 Substitution Prop. -2y -2y Sub. Prop of = 3y + 6 = 21 – 6 – 6 Sub. Prop of = 3y = 15 3 3 Div. Prop of = y = 5

  13. Seg. Add. Postulate PQ + QR = PR 3n + 25 = 9n – 5 Substitution Prop. -3n -3n Sub. Prop of = 25 = 6n– 5 +5 +5 Add. Prop of = 30= 6n 6 6 5 = n Div. Prop of =

  14. Worksheet 2.6 – Part 1

  15. Homework • Worksheet 2.6 – Part 2

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