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Geometry

Geometry. 2.2 Properties of Equality: POE’s & Properties of Congruence: POC’s. Addition POE. If a = b and c = d, then a + c = b + d ½ = 0.5 and 2 = 2.0, thus ½ + 2 = 0.5 + 2.0. Subtraction POE. If a = b and c = d, then a - c = b - d 10 = 10.0 and ¼ = 0.25,

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Geometry

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  1. Geometry 2.2 Properties of Equality: POE’s & Properties of Congruence: POC’s

  2. Addition POE • If a = b and c = d, then a + c = b + d • ½ = 0.5 and 2 = 2.0, thus ½ + 2 = 0.5 + 2.0

  3. Subtraction POE • If a = b and c = d, then a - c = b - d • 10 = 10.0 and ¼ = 0.25, thus 10 – 1/4 = 10.0 – 0.25

  4. Multiplication POE • If a = b, then ca = cb • ¾ = 0.75, thus 100(¾) = 100(0.75)

  5. Division POE • If a = b and c 0, then a/c = b/c • 8 = 8.0 and 2 0, thus 8/2 = 8.0/2

  6. Substitution POE • If a = b, then either a or b may be substituted for the other in an equation or inequality. • If x = 5, then (x) + 10 = (5) + 10

  7. Distributive POE • a(b + c) = ab + ac • 5(x + 3) = 5x + 15

  8. Reflexive • Reflexive POE a = a • Reflexive POC and

  9. Symmetric • Symmetric POE If a = b, then b = a • Symmetric POC If , then If , then

  10. Transitive Property • Transitive POE If a = b, and b = c, then a = c • Transitive POC If , and then If , and then

  11. A Few Together • Please turn to page 40. Let’s try #1-10. • Reflexive POE • Transitive POE • Symmetric POE • Subtraction POE • Division POE • Multiplication POE • Distributive POE • Addition POE • Substition POE • Transitive POE

  12. 1) 2/3B = 8 – 2B 2) 2B = 3(8 – 2B) 3) 2B = 24 – 6B 4) 8B = 24 5) B = 3 1) Given 2) Mult. POE 3) Distr. POE 4) Add. POE 5) Div. POE 5) Justify each step(from the HW)

  13. . S . I . T 1) ST = RN 2) ST = SI + IT RN = RU + UN 3) SI + IT = RU + UN 4) IT = RU 5) SI = UN 1) Given 2) Segment Add. Post. 3) Subst. POE 4) Given 5) Subtr. POE CE 12) Complete the ProofGiven ST = RN; IT = RUProve: SI = UN . R . U . N

  14. Homework • 2.2 CE #12 WE #1-11

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