Geometry - Deductive Reasoning - Chapt 2

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Mamadams
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290758
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Geometry - Deductive Reasoning - Chapt 2
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2014-12-06 17:36:33
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Geometry
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  1. Conditional - a statement that can be written in if-then form

    a.  hypothesis - the given information
    b.  conclusion - what you are trying to prove

                 symbolic:    p  ⇒  q

  2. Negation - opposite of the original statement. it is or it isn't

                    symbolic:   ~ p
  3. Counterexample - an example that proves that a statement is false.

  4. Converse - statement made by exchanging the hypothesis and conclusion.
                   
    Inverse - statement made by negating both the hypothesis and conclusion

    Contrapositive - statement made by negating both the hypothesis and conclusion of the converse.

  5. Equivalent statements - same truth value

    Rules:
    contrapositive and counterexample always the same

    inverse and converse always the same.
  6. Logic rule:  p ⇒ q, if given q ⇒ p


    All cows eat grass.

    Elsey is a cow then she sat grass.
  7. biconditional - combining a true conditional with its true converse using if and only if.
  8. State the property that justifies each statement.

    1.  If m <1 = m <2 , then m <2 = m <1.

    2.  If m<1 = 90 and m <2 = m<1, then m <2 = 90.

    3.  If AB = RS and RS = WY, then AB = WY.

    4.  If AB = CD, then 1/2AB = 1/2CD.

    5.  If m <1 + m <2 = 110 and m <2 = m <3, then m <1 + m <3 = 110.

    6.  RS = RS

    7.  If AB = RS and TU = WY, then AB + TU = RS + WY.
  9. Vertical angles - two non-adjacent angles formed by intersecting lines.

  10. Vertical angles are congruent.

  11. Complementary angles - two angles whose sum is 90°.

  12. Theorem 2-8

    Congruent Complements Theorem

    If two angles are complements of the same < or congruent < then the angles are congruent.
  13. supplementary angles - two angles whose sum is 180°.
  14. Theorem 2-7

    Congruent Supplements Theorem

    If two angles are supplements of the same < or congruent < then the angles are congruent.
  15. Linear pair

    *  two adjacent angles whose non common sides are  line

    *  always supplementary (180°)

  16. Perpendicular lines: two lines that intersect to form a right angle. (90°)

  17. Theorem 2-4

    If two lines are perpendicular then they form congruent adjacent angles.

  18. Theorem 2-5 converse to Theorem 2-4

    If 2 lines form congruent adjacent angles then lines are perpendicular.


    If <3 and <4 are congruent then a is perpendicular to b
  19. Theorem 2-6

    If the exterior sides of two adjacent acute angles are perpendicular then the angles are complementary.
  20. Inductive reasoning - basing a conclusion on observations only. This doesn't have to be true.

    Deductive reasoning - basing a conclusion on a fact.  If the hypothesis is true, so is the conclusion.
  21. Law of Detachment: if p → q is true and p is true then q is true.
  22. Law of Syllogism: if p → q and q → r are true, then p → r is true.

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