Answers to the HW

p. 75 #10-20 even, 25-28 all, 55 & 5610. If an object weighs one pound, then it weights

16 ounces.

12. If a fish is a blue trunkfish, then it lives in the waters of a coral reef.

14. True 16. True

18. If 1 is obtuse, then 1 measures 123.

20. If I go to the mall, then it is not raining.

25. One 26. two 27. line 28. a line

55. D 56. D

Answers to the HWp. 82 #14 - 26 even, 54 & 55

14. True 16. true 18. 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.

26. Terry could live in Orlando, FL, not in Tampa, FL.

54. D 55. B

You may use your notes1. Identify the conclusion. If the weather is warm, then we

should go swimming.

2. Write the contrapositive. If you like purple, then you will like this shirt.

3. Rewrite the biconditional statement as a conditional statement and its converse. Two segments are congruent if and only if they have the same measure.

4. Write the inverse. If you like hockey, then you go to the hockey game.

5. Give a counterexample that demonstrates that the converse of the statement is false. If a vehicle is a car, then it has wheels.

2.3 Deductive ReasoningObjective: Apply logic to true statements to

make valid conclusions

Let p be “Today is Tuesday” and q be “There is school.

1. What is p q ? 2. What is ~p ~q ?

3. What is q p ?

4. What is ~q ~p ?

If today is Tuesday, then there is school.

If today is not Tuesday, then there is no school.

If there is school, then today is Tuesday.

If there is no school, then today is not Tuesday.

Deductive Reasoning

Deductive Reasoning uses facts, definitions, and accepted properties to write logical arguments (proofs).

How is this different from Inductive Reasoning?

Law of Detachment

If a conditional statement is true and the hypothesis is true,

then the conclusion is automatically true.

p qp is true

q is true

If a triangle is equilateral, then the measure of each angle is 60.

Triangle ABC is an equilateral triangle.

The measure of each angle is 60.

EX 1: Use the Law of Detachment to determine a conclusion.

If two lines are parallel, then the lines do not intersect.

k is parallel to m.

k and m do not intersect.

EX 2: Use the Law of Detachment to determine a conclusion.

If Robby is taller than Ben, then Robby is at least 6 feet tall.

Ben is older than Robby.

NO VALID CONCLUSION!

EX 3: Use the Law of Detachment to determine a conclusion.

Law of SyllogismSimilar to the transitive property in algebraHas 3 statements:

1st and 2nd are true, 2nd and 3rd are true, so 1st and 3rd must also be true.

p q is trueq r is true

p is truer

EX 4: Use the Law of Syllogism to determine a conclusion.

If Donnie asks Pam, then she will say yes.

If she says yes, then they will get married.

If Donnie asks Pam, then they will get married.

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.

If Tim gets stung by a bee, then he will go to the hospital.

EX:5 Use the Law of Syllogism to determine a conclusion.

If Jay doesn’t work hard, then he will not play.

If he doesn’t play, then he will quit the team.

If Jay doesn’t work hard, then he will quit the team.

EX 6: Use the Law of Syllogism to determine a conclusion.

If Susan screams, then the dog will run away.

If the dog licks Susan, then Susan will scream.

NO VALID CONCLUSION!!

EX 7: Use the Law of Syllogism to determine a conclusion.

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.

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.

2.4 Reasoning with Algebraic Properties

Objective: Use Properties of Algebra to explain multi-step equations

Algebraic Properties of Equality

p. 96 and 98

KNOW THEM!

Let a, b, and c be real numbers

Addition Property

Subtraction Property

Multiplication Property

Division Property

If a = b, then a + c = b + cadd the same thing to both sides of an eqn. & they will still be equal

If a = b, then a - c = b - c

If a = b, then ac = bc

subtract the same thing from both sides of an eqn. & they will still be equal

multiply the same thing to both sides of an eqn & they will still be equal

divide the same thing from both sides of an eqn & they will still be equal

If a = b and c 0, then

a c = b c

Let a, b, and c be real numbers

Reflexive Property

Symmetric Property

Transitive Property

Substitution Property

For any real number a, a = aA number, length, or measure will always equal itself

If a = b, then b = a

If a = b and b = c then a = c

If two things are equal then order does not matter

This is true by the Law of Syllogism

Think about substituting 3 in for x in an equation when x = 3

If a = b, then a can be substituted for b in any equation or expression

Write a reason for each step.

10 2 3 2 4x x 10 2 3 6 4x x 10 2 3 2x x 10 5 2x

5 12x 12

5x

Given

Distributive Property

Addition Property

Subtraction Property

Subtraction Property

Division Property

Use the property to complete the statement.

1. Addition property of equality: If AB = 5, then 10 + AB = ____.

2. Multiplication property of equality: If mC = 30, then ____ (mC) = 15 .

15

1/2

AF

mMJC = mDCF

5(3)

3. Reflexive property of equality: AF = ___.

4. Symmetric property of equality: If mDCF = mMJC, then ________________.5. Transitive property of equality: If YZ = DB and DB = JK, then _________.

6. Substitution property of equality: If MN = 3, then 5(MN) = _____.

YZ = JK

Homework:

p. 91-93 (13 problems) #8-32 even

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