Reasoning & Truth Values
Conditionals and Their Buddies
Algebraic & Geometry Proof
Random
100
What is next in the pattern? 5, -2, -9, -16,...
-23
100
Rewrite the statement in its conditional form: When it rains, there are clouds in the sky.
If it is raining, then there are clouds in the sky.
100
Solve the equation and write a justification for each step. x + 5 = 12
Given
Subtraction Property
100
Is the following an example of what type of angle?
Complimentary Angles
200
Show that the conjecture is false by finding a counterexample. If a food is a fruit, then it is an apple.
Answers may vary.
EX: Pear, banana, etc...
200
Write the converse of the statement: "If two angles are congruent, then they have the same measure."
If two angles have the same measure, then they are congruent.
200
Write a justification for each step: 4(x - 7) = 3x + 8
(1) 4(x - 7) = 3x + 8
(2) 4x - 28 = 3x + 8
(3) 4x - 36 = 3x
(4) -36 = -x
(5) 36 = x
(1) Given
(2) Distributive Property
(3) Subtraction Property
(4) Subtraction Property
(5) Division Property
200
Name the following postulate?
Angle Addition Postulate
300
Determine if the conditional is true. If false, give a counterexample:
If you have a dog, then it is spot.
False, you can have a dog whose name is not spot.
300
Write the contrapositive of the statement: "If two angles are supplements of the same angle then the angles have the same measure."
"If two angles do not have the same measure, then they are not supplements of the same angle."
300
Given: 18x - 2(3x + 1) = 5x - 16
Prove: x = -2
(1) 18x - 2(3x + 1) = 5x - 16
(2) 18x - 6x - 2 = 5x - 16
(3) 12x - 2 = 5x - 16
(4) 7x - 2 = -16
(5) 7x = -14
(6) x = -2
(1) Given
(2) Distributive Property
(3) Combine Like Terms
(4) Subtraction Property
(5) Addition Property
(6) Division Property
300
Draw the next figure?
400
Determine whether the conjecture.
If Lewis earns a scholarship, he can go to college. Lewis earns a scholarship.
Lewis can go to college.
Law of Detachment
400
Write the converse, inverse, and contrapositive:
Conditional: If a figure is a square, then it is a quadrilateral.
Converse: If a figure is quadrilateral, then it is a square.
Inverse: If a figure is not a square, then it is not a quadrilateral.
Contrapositive: If a figure is not a quadrilateral, then it is not a square.
400
Given: AC=39
Prove: x=2
Statement /Reason
AC=39/Given
AB+BC=AC/Segment Addition Postulate
9x+7-3x+20=39/Substitution
6x+27=39/Combine Like Terms
6x=12/Subtraction Property
x=2/Division Property
400
What are the values for angle q and e?
Angle E=45 degrees
Angle q=90 degrees
500
Determine the conjecture
If a whole number ends in 0, then it is divisible by 2. If a whole number is divisible by 2, then it is even.
If a whole number ends in 0, then it is an even number.
Law of Syllogism
500
Write the converse, inverse and contrapositive, and determine the truth values of the conditional, converse, inverse, and contrapositive:
Conditional: If you play baseball, then you are an athlete.
Conditional: If you play baseball, then you are an athlete. - True
Converse: If you are an athlete, then you play baseball. - False, you can play any other sport.
Inverse: If you do not play baseball, then you you are not an athlete. -False, just because you do not play does not mean you are not an athlete if you play another sport.
Contrapositive: If you are not an athlete, then you do not play baseball. -True
500
Write a two column proof:
Given: <XYZ=180
Prove: <OYZ=67
Answers May Vary :
Statement /Response
<xyz=180/Given
<xyo+<oyz=<xyz/Angle Addition Postulate
3x+5+2x-5=180/Substitution
5x=180/Combine Like Terms
x=36/Division Property
<oyz=2x-5/Given
<oyz=2(36)-5/Substitution
<oyz=72-5/Distribution
<oyz=67/Combine Like Terms
500
What is the value of x and angle B?
x=8 degrees
Angle B=116 degrees