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Deductive Reasoning

Deductive Reasoning. Geometry Chapter 2. Vocabulary . Converse-formed by interchanging the hypothesis and the conclusion Statement: If p, then q Converse: If q, then p. Vocabulary. Counterexample-an example that can be found for which the hypothesis is true and the conclusion is false.

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Deductive Reasoning

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  1. Deductive Reasoning Geometry Chapter 2

  2. Vocabulary • Converse-formed by interchanging the hypothesis and the conclusion Statement: If p, then q Converse: If q, then p

  3. Vocabulary • Counterexample-an example that can be found for which the hypothesis is true and the conclusion is false.

  4. Conditional • If-then Statements/Conditional Statements • “If B is between A and C, then AB+BC=AC • If Katie eats a lot, then Katie is fat. Hypothesis is in Red Conclusion is in Blue

  5. Biconditional • A statement that contains the words “if and only if”. • 3x=12 if and only if, x=4 • Katie gets hyper in the morning if and only if she drinks coffee

  6. Properties from Algebra Geometry Ch.2 Section 2

  7. Properties of Equality Addition Property If a=b and c=d, then a+c=b+d Subtraction Property If a=b and c=d then a-c=b-d Multiplication Property If a=b, then ca=cb Division Property If a=b and c≠0, then a/c=b/c

  8. Properties from Algebra Substitution Property If a=b, then either a or b may be substitute for the other in any equation (or inequality). Reflexive Property a=a Symmetric Property If a=b, then b=a Transitive Property If a=b Distributive Property a(b+c)=ab+ac

  9. Properties of Congruence • Reflexive Property – • Symmetric Property- • Transitive Property-

  10. Proving Theorems Geometry Ch.2 Lesson 3

  11. Vocabulary • Theorem-statements that are proved • Postulates-statements that are accepted without proof

  12. Midpoint Theorem • If M is the midpoint of line AB, then AM=1/2AB and MB=1/2AB

  13. Angle Bisector Theorem If ray AD is the bisector of <CAB, then m<CAD=1/2m<CAB and m<DAB=1/2m<CAB

  14. Proofs/Deductive Reasoning

  15. Theorems about Angles and Perpendicular Lines Geometry Ch. 2 Lesson 4

  16. Vocabulary • Complementary Angles-two angles whose measures have the sum of 90 degrees. • Supplementary Angles-two angles whose measures have the sum of 180 degrees • Vertical Angles-two angles such that the sides of one angle are opposite rays to the sides of the other angle.

  17. Theorem • Vertical Angles are congruent

  18. Perpendicular Lines Geometry Chapter 2 Lesson 5

  19. Vocabulary • Perpendicular Lines-two lines that intersect to form right angles (90 degree angles).

  20. Theorem • If two lines are perpendicular, then they form congruent adjacent angles

  21. Theorem • If two lines form congruent adjacent angles, then the lines are perpendicular.

  22. Theorem • If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.

  23. Planning A Proof Chapter 2 Lesson 6

  24. Theorem • If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent.

  25. Theorem • If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent.

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