# Geometry - Deductive Reasoning - Chapt 2

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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.
 Author: Mamadams ID: 290758 Card Set: Geometry - Deductive Reasoning - Chapt 2 Updated: 2014-12-06 22:36:33 Tags: Geometry Folders: Description: review Show Answers: