1. Answers to the HW p. 75 #10-20 even, 25-28 all, 55 & 56
10. If an object weighs one pound, then it weights 16 ounces.
If a fish is a blue trunkfish, then it lives in the waters of a coral reef.
True True
18. If 1 is obtuse, then 1 measures 123.
If I go to the mall, then it is not raining.
25. One two line a line
55. D D

2. Answers to the HW p. 82 #14 - 26 even, 54 & 55
14. True true true
20. (conditional) If two angles are congruent, then they have the same measure; (converse) If two angles have the same measure, then they are congruent.
22. (conditional) If two lines are perpendicular, then they intersect to form right angles; (converse) If two lines intersect to form right angles, then the two lines are perpendicular.
24. A 100 angles is obtuse, but doesn’t measure 94.
Terry could live in Orlando, FL, not in Tampa, FL.
54. D B

3. You may use your notes
Identify the conclusion. If the weather is warm, then we should go swimming.
Write the contrapositive. If you like purple, then you will like this shirt.
Rewrite the biconditional statement as a conditional statement and its converse. Two segments are congruent if and only if they have the same measure.
Write the inverse. If you like hockey, then you go to the hockey game.
Give a counterexample that demonstrates that the converse of the statement is false. If a vehicle is a car, then it has wheels.

4. Objective: Apply logic to true statements to make valid conclusions
2.3 Deductive Reasoning
Objective: Apply logic to true statements to make valid conclusions

5. Let p be “Today is Tuesday” and q be “There is school.
1. What is p  q ?
If today is Tuesday, then there is school.
2. What is ~p  ~q ?
If today is not Tuesday, then there is no school.
3. What is q  p ?
If there is school, then today is Tuesday.
4. What is ~q  ~p ?
If there is no school, then today is not Tuesday.

6. How is this different from Inductive Reasoning?
Deductive Reasoning
Deductive Reasoning uses facts, definitions, and accepted properties to write logical arguments (proofs).
How is this different from Inductive Reasoning?

7. Law of Detachment
If a conditional statement is true and the hypothesis is true, then the conclusion is automatically true.

8. EX 1: Use the Law of Detachment to determine a conclusion.p q
If a triangle is equilateral, then the measure of each angle is 60.
Triangle ABC is an equilateral triangle.
p is true
The measure of each angle is 60.

9. EX 2: Use the Law of Detachment to determine a conclusion.p q
If two lines are parallel, then the lines do not intersect.
k is parallel to m.
p is true
 k and m do not intersect.

10. EX 3: Use the Law of Detachment to determine a conclusion.p
If Robby is taller than Ben, then Robby is at least 6 feet tall.
Ben is older than Robby. q
r is true
NO VALID CONCLUSION!

11. Law of Syllogism
Similar to the transitive property in algebra
Has 3 statements:
1st and 2nd are true, 2nd and 3rd are true, so 1st and 3rd must also be true.

12. EX 4: Use the Law of Syllogism to determine a conclusion.p q
If Donnie asks Pam, then she will say yes.
If she says yes, then they will get married. q r
If Donnie asks Pam, then they will get married.

13. EX:5 Use the Law of Syllogism to determine a conclusion.p q
If Tim gets stung by a bee, then he will get very ill.
If he gets very ill, then he will go to the hospital. r q
If Tim gets stung by a bee, then he will go to the hospital.

14. EX 6: Use the Law of Syllogism to determine a conclusion.p q
If Jay doesn’t work hard, then he will not play.
If he doesn’t play, then he will quit the team. r q
If Jay doesn’t work hard, then he will quit the team.

15. EX 7: Use the Law of Syllogism to determine a conclusion.p q
If Susan screams, then the dog will run away.
If the dog licks Susan, then Susan will scream. r p
NO VALID CONCLUSION!!

16. Use the true statements to determine whether the conclusion is true or false.
If it looks like rain, then I will bring my umbrella to school with me.
If there are clouds in the sky and the sky is dark, then it looks like rain.
If I bring my umbrella to school with me, then I will hang it in the classroom closet.
This morning, there are clouds in the sky and the sky is dark.
Conclusion: My umbrella is hanging in the classroom closet.

17. In order…
This morning, there are clouds in the sky and the sky is dark.
If there are clouds in the sky and the sky is dark, then it looks like rain.
If it looks like rain, then I will bring my umbrella to school with me.
If I bring my umbrella to school with me, then I will hang it in the classroom closet.
Conclusion: My umbrella is hanging in the classroom closet.
TRUE

18. 2.4 Reasoning with Algebraic Properties
Objective: Use Properties of Algebra to explain multi-step equations

19. Algebraic Properties of Equality
p. 96 and 98
KNOW THEM!

20. Multiplication Property
Let a, b, and c be real numbers
If a = b, then a + c = b + c
Addition Property
add the same thing to both sides of an eqn. & they will still be equal
Subtraction Property
If a = b, then a - c = b - c
subtract the same thing from both sides of an eqn. & they will still be equal
Multiplication Property
If a = b, then ac = bc
multiply the same thing to both sides of an eqn & they will still be equal
Division Property
divide the same thing from both sides of an eqn & they will still be equal

21. Substitution Property
Let a, b, and c be real numbers
Reflexive Property
For any real number a, a = a
A number, length, or measure will always equal itself
Symmetric Property
If a = b, then b = a
If two things are equal then order does not matter
Transitive Property
If a = b and b = c then a = c
This is true by the Law of Syllogism
Substitution Property
If a = b, then a can be substituted for b in any equation or expression
Think about substituting 3 in for x in an equation when x = 3

22. To solve the equation 10y + 5 = 25 ,put these steps in order
Given
y = 2
10y =
Subtraction Prop.
10y = 20
10y = 20
Simplify
10y + 5 = 25
Division Property
y = 2
Simplify

23. Write a reason for each step.
Given
Distributive Property
Addition Property
Subtraction Property
Subtraction Property
Division Property

24. Use the property to complete the statement.
1. Addition property of equality: If AB = 5, then 10 + AB = ____. 15
2. Multiplication property of equality: If mC = 30, then ____ (mC) = 15 .
1/2
3. Reflexive property of equality: AF = ___. AF
4. Symmetric property of equality: If mDCF = mMJC, then ________________.
mMJC = mDCF
5. Transitive property of equality: If YZ = DB and DB = JK, then _________.
YZ = JK
6. Substitution property of equality: If MN = 3, then 5(MN) = _____.
5(3)

25. WY = XZ Show that WX = YZ WY = XZ WY = WX + XY XZ = XY + YZ
Given
WY = XZ
Segment Addition Postulate
WY = WX + XY
Segment Addition Postulate
XZ = XY + YZ
WX + XY = XY + YZ
Substitution Prop. Of Equality
Subtraction Prop. Of Equality
WX = YZ

26. Substitution prop of equality
Banked turns help the cars travel around the track at high speeds. The angles provide an inward force that helps keep the cars from flying off the track. Given the following information about the four banked turns at the Talladega Superspeedway racetrack in Alabama, find the measure of angle 4
Given
Given
Substitution prop of equality
Subtraction prop of equality =
Given
Transitive prop of equality
Substitution prop of equality

27. p.99–101 (9 problems) #4-8, 10-14 even, 32 a-e
Homework:
p (13 problems) #8-32 even
p.99–101 (9 problems) #4-8, even, 32 a-e