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Math 2 Geometry Based on Elementary Geometry , 3 rd ed, by Alexander & Koeberlein

Math 2 Geometry Based on Elementary Geometry , 3 rd ed, by Alexander & Koeberlein. 1.5 Introduction to Geometric Proof. Properties of Equality. Addition property of equality If a = b , then a + c = b + c Subtraction property of equality If a = b , then a – c = b – c

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Math 2 Geometry Based on Elementary Geometry , 3 rd ed, by Alexander & Koeberlein

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  1. Math 2 GeometryBased on Elementary Geometry, 3rd ed, by Alexander & Koeberlein 1.5 Introduction to Geometric Proof

  2. Properties of Equality Addition property of equality If a = b, then a + c = b + c Subtraction property of equality If a = b, then a – c = b – c Multiplication property of equality If a = b, then a·c = b·c Division property of equality If a = b and c  0, then a/c = b/c

  3. Properties of Inequality Addition property of inequality If a > b, then a + c > b + c Subtraction property of inequality If a > b, then a – c > b – c Multiplication property of inequality If a > b, and c > 0, then a·c > b·c Division property of inequality If a > band c > 0, then a/c > b/c

  4. More Algebra Properties Distributive property a(b + c) = a·b + a·c Substitution property If a = b, then a replaces b in any equation Transitive property If a = b and b = c, then a = c

  5. Given: 2(x – 3) + 4 = 10 Prove: x = 6 Proof

  6. Given: 2(x – 3) + 4 = 10 Prove: x = 6 Proof

  7. Given: 2(x – 3) + 4 = 10 Prove: x = 6 Proof

  8. Given: 2(x – 3) + 4 = 10 Prove: x = 6 Proof

  9. Given: 2(x – 3) + 4 = 10 Prove: x = 6 Proof

  10. Given: 2(x – 3) + 4 = 10 Prove: x = 6 Proof

  11. Given: 2(x – 3) + 4 = 10 Prove: x = 6 Proof

  12. Given: 2(x – 3) + 4 = 10 Prove: x = 6 Proof

  13. Given: A-P-B on seg AB Prove: AP = AB - PB Proof

  14. Given: A-P-B on seg AB Prove: AP = AB - PB Proof

  15. Given: A-P-B on seg AB Prove: AP = AB - PB Proof

  16. Given: A-P-B on seg AB Prove: AP = AB - PB Proof

  17. Given: A-P-B on seg AB Prove: AP = AB - PB Proof

  18. • M • N • P • Q Given: MN > PQ Prove: MP > NQ Proof

  19. • M • N • P • Q Given: MN > PQ Prove: MP > NQ Proof

  20. • M • N • P • Q Given: MN > PQ Prove: MP > NQ Proof

  21. • M • N • P • Q Given: MN > PQ Prove: MP > NQ Proof

  22. • M • N • P • Q Given: MN > PQ Prove: MP > NQ Proof

  23. • M • N • P • Q Given: MN > PQ Prove: MP > NQ Proof

  24. • M • N • P • Q Given: MN > PQ Prove: MP > NQ Proof

  25. • M • N • P • Q Given: MN > PQ Prove: MP > NQ Proof

  26. • M • N • P • Q Given: MN > PQ Prove: MP > NQ Proof

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