1. Angles, Angle Pairs, Conditionals, Inductive and Deductive Reasoning
Review
Angles, Angle Pairs, Conditionals, Inductive and Deductive Reasoning

2. 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 – x + 21 = 180
2x – 1 + 3x + 2 = 90

3. 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 = _____

4. 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.

5. 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.

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

7. 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

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

9. 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.

10. 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) _________________

11. 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.

12. 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