Reasoning
Logic
Conditional Statements
Algebraic Proof
Proving Relationships
100
What number is next? What's the rule?
1, 3, 9, 27, 81,__
243 and times 3
100
What's the negation of the statement?
Strawberries are the best fruit.
Strawberries are not the best fruit.
100
What's the statement as a conditional?
Zero is neither prime nor composite.
If a number is neither prime nor composite, then its is zero.
100
What's the property that justifies the statement?
If m<1 =m<2, then m<2=m<1.
Symmetric Property
100
What is the m<POQ? What theorem proves this? 
m<POQ=93.64
Supplement Theorem
200
What is the measure of <1 and <2?
m<1=90°
m<2=90°
200
What's the compound statement? What's the truth value?
p and q
p: 17+7=24
q: A heptagon has 7 sides
True
17+7=24 and a heptagon has 7 sides
200
Determine the truth value of the conditional statement. (Counterexample)
If two angles are supplementary, then one is acute.
False, you can have 2 right angles.
200
What's the property that justifies the statement?
If AB=CD, then 7AB=7CD.
Multiplication
200
What is the measure of angle MLN? What theorem proves this?
m<MLN=58.49
Compliment theorem
300
Is the conclusion valid? Why?
If the sum of the measures of two angles is 180, then the angles are supplementary. <1 and <2 are a linear pair.
Conclusion: <1 and <2 are supplementary.
No, the hypothesis don't match.
300
What's the compound statement? What's the truth value?
p V q
p:Tomatoes are fruits.
q: A circle is a polygon.
True
Tomatoes are fruits or a circle is a polygon
300
What's the statement as a bi-conditional?
If the sun is out, then it is day.
The sun is out if and only if it is day.
300
What does x equal?
x=49
300
1. AB=CD 1. ___________
2. ___________ 2. Reflexive
3. AB+BC=BC+CD 3. Addition prop. of equality
4. AB+BC=AC/BC+CD=BD 4._______________
5. AC=BD 5. __________
1. Given
2. BC=BC
4. Segment addition postulate
5. Substitution
400
Is the conclusion valid? If so draw a valid conclusion.
If an animal is a dolphin, then its scientific name is Delphinus.
If an animals scientific name is Delphinus, then it lives in the ocean.
Yes, Law of Syllogism
If an animal is a dolphin, then it lives in the ocean.
400
What's the last column of the Truth Table?
400
What is the inverse of the conditional statement?
If it is raining, then the grass is wet.
If it is not raining, then the grass is not wet.
400
Two column proof for:
500
Is the conjecture false? If so give a counterexample.
If a polygon doesn't have right angles, then it is a parallelogram.
False, a regular hexagon
500
How many people took Math but not Chemistry?
90 people
500
What is the contrapositive of the conditional statement?
If two angles are congruent, then they have the same measure.
If they do not have the same measure, then the two angles are not congruent.
500
Given: 3x+12=8x-18
Prove:x=6
1. 3x+12=8x-18 1._______
2. 3x=8x-30 2._______
3. __________ 3. Subtract
4. __________ 4. _______
1. Given
2.Subtract
3. -5x=-30
4. x=6 and Divide
500
What's the measure of angle 1 and 2? What's x?
x=38
m<1=48
m<2=132