Angles, Angle Pairs, Conditionals, Inductive and Deductive Reasoning

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Presentation transcript:

Angles, Angle Pairs, Conditionals, Inductive and Deductive Reasoning 1.5-1.6-2.1-2.2 Review Angles, Angle Pairs, Conditionals, Inductive and Deductive Reasoning

Complementary, Supplementary, or Congruent 3x + 2 2x – 1 13x + 21 7x – 1 5x + 10 7x – 30 Complementary Congruent… (Vertical) Supplementary…(Linear Pair) 5x + 10 = 7x – 30 7x – 1 + 13x + 21 = 180 2x – 1 + 3x + 2 = 90

50 1 is a complement of 2, if m1 = 40, then m2 = _____ 110 1 is a supplement of 2, if m1 = 70, then m2 = _____

Conditionals If p then q hypothesis conclusion If an angle is a right angle, then it measures exactly 90. If it’s raining, then it’s wet.

Conditionals don’t have to say “if…then” but can be converted. An angle that is greater than 90 is an obtuse angle. _______________________________________ If an angle is greater than 90, then it’s an obtuse angle. Free phone with every service agreement. ____________________________________________ If you buy a service agreement, then you will get a new phone.

Negation p is a statement p is a negation of the statement 1. p: it’s raining p: it’s not raining 2. p: it’s not wet p: it’s wet

Related Conditionals Conditional If p, then q If p, then q If it’s raining then it’s wet. T If q, then p If it’s wet, then it’s raining. If q, then p Converse If q, then p F If p, then q If it’s not raining, then it’s not wet. If p, then q Inverse If p, then q F Contrapositive If q, then p If q, then p If it’s not wet, then it’s not raining. If q, then p T If False give a Counterexample If False give a Counterexample Logically Equivalent Have the same truth value Logically Equivalent Have the same truth value

Deductive Reasoning Two types of Deductive Reasoning are: Detachment 1. Law of __________________ Detachment 2. Law of __________________ Syllogism

Law of Detachment If pq is true, and p is true, then q is also true. EX) (1) If it’s raining, then it’s wet. (2) On Thursday it was raining. (3) Therefore, on Thursday it was wet.

Law of Detachment If pq is true, and p is true, then q is also true. EX) (1) If the measure of an angle is greater than 90, then it is obtuse. CAB is greater than 90. (2) _________________ CAB is obtuse. (3) _________________

Law of Syllogism If p  q and q  r, then p  r Fancy way to say transitive EX) (1) If 1 and 2 form a linear pair, then they are supplementary. p q q r (2) If 1 and 2 are supplementary, then m1 + m2 = 180. p r (3) ____________________________________________________ If 1 and 2 form a linear pair, then m1 + m2 = 180.

Law of Syllogism If p  q and q  r, then p  r EX) (1) If two lines are perpendicular, then they form a right angle. p q q r (2) If a right angle is formed, then the measure is 90. r p (3) __________________________________________________ If two lines are perpendicular, then the measure is 90