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Algebraic Proof Properties - Justifying Statements and Proofs

This chapter explores algebraic proof properties and provides examples of how to justify statements and proofs. Learn about equations, angles, and congruent segments.

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Algebraic Proof Properties - Justifying Statements and Proofs

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  1. Chapter 2.6 Algebraic Proof

  2. Properties you need to know!

  3. State the Property that justifies each statement • If 4 + (-5) = -1, Then x + 4 + (-5) = x – 1 • If 5 = y, Then y = 5 • If 2a = -18, Then a= - 9

  4. Statements Reasons Prove that if 2x + 5 = 15, then x = 5

  5. Statements Reasons Example 1 Justify Each Step When Solving an Equation Prove that if 2(5 – 3a) – 4(a + 7) = 92, then a = -11

  6. Statements Reasons Prove that if -3(a+3) + 5(3-a) = -50, then a = 7

  7. Postulates

  8. Concept

  9. If A B, mB = 2mC, and mC = 45, then mA = 90. Write a two-column proof to verify this conjecture. Example 3 Write a Geometric Proof

  10. Proof: Statements Reasons mA = 2(45) 4. Substitution 4. 2.mA = mB 2. Definition of angles A B; mB = 2mC; mC = 45 1. Given 1. 5. mA = 90 5. Substitution 3. Transitive Property of Equality 3. mA = 2mC Example 3 Write a Geometric Proof

  11. Example 3

  12. Proof: 1. Given 1. Statements Reasons ? 2. 2. _______________ 3.AB = RS 3. Definition of congruent segments 4. AB = 12 5. RS = 12 4. Given 5. Substitution Example 3

  13. Write a two column proof for the conjecture. If CD = EF, and CD=3y – 9, and EF = 15, then y = 8

  14. Example 2 Write an Algebraic Proof Begin by stating what is given and what you are to prove.

  15. Try it! • Pg. 138 #3A • Pg. 139 #7

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