Inductive Reasoning
Conditional Statements
Deductive Reasoning
Biconditional Statements
Proofs
100
1/6, 1/3, 1/2, 2/3...
What is 5/6
100
Determine if the conjecture is true. If false, write a counterexample. If two angles are adjacent, then they have a common ray.
True.
100
If 5c = 8y, then 2w = -15. If 5c = 8y, then x = 17. Conjecture: If 2w = -15, then x =17. Is this valid by the Law of Syllogism?
No!
100
Is the following biconditional true: x < 0 if and only if the value of x4 is positive.
False, x can be a positive number.
100
Solve each equation and write a justification for each step. -47 = 3x - 59
Given Add. Prop. of = Div. Prop. of =
200
The sum of an even number and an odd number is _______. The square of a natural number is _________.
odd, positive.
200
Determine if the conjecture is true. If false, write a counterexample. If you multiply two irrational numbers, the product is irrational.
False, square root of 2 times the square root of two.
200
If two lines are distinct, then there is one line through them. A and B are distinct points. What conjecture can I make?
There is one line through the points.
200
True or false: If the measure of one angle of a triangle is 90º, then the triangle is a right triangle.
True
200
Identify the property that justifies the statement: 2x = 9 and 9 = y. So 2x = y.
Transitive Property
300
Determine if the conjecture is true. If false, write a counterexample. If C is the midpoint of AB, then AC is congruent to BC.
True.
300
Write the inverse of "If ∠X is a right angle, then m∠X= 90º." and find the truth value.
If ∠X is not a right angle, then m∠X is not 90º. True.
300
Is the conjecture valid by the Law of Detachment? Given: If you want to go on a field trip, you must have a signed permission slip. Zola has a signed permission slip. Conjecture: The area of a rectangle is 12 ft.
Not valid.
300
Complete each statement to form a true biconditional: Two angles are ________ if and only if the sum of their measures is 90º
Complementary
300
Solve the equation and justify each step. m/-5 + 3 = -4
Given Subtraction Prop. of = Mult. Prop. of =
400
Determine if the conjecture is true. If false, write a counterexample. There are 28 days in February.
False, during a leap year.
400
Write the contrapositive of "If x is a whole number, then x = 2" and find the truth value.
If x doesn't equal 2, then x is not a whole number. False, there are other whole numbers besides 2.
400
Determine if the conjecture is valid by the Law of Syllogism. Given: If a figure is a square, then the figure is a rectangle. If a figure is a square, then it is a parallelogram. Conjecture: If a figure is a parallelogram, then it is a rectangle.
Not valid.
400
The area of a square is equal to s2 iff the perimeter of the square is _________.
4s
400
Write a justification for each step, given that ∠1 and ∠2 are complementary, and ∠1 is congruent to ∠3. 1. ∠1 and ∠2 are complementary 2. m∠1 + m∠2 = 90º 3. ∠1 congruent to ∠3 4. m∠1 = m∠3 5. m∠3 + m∠2 = 90º 6. ∠3 and ∠2 comp.
1. Given 2. Def. of comp. angles 3. Given 4. Def. of congruent angles 5. Substitution 6. Def. of comp. angles
500
Determine if the conjecture is true. If false, write a counterexample. If 2x + 3 = 15, then x = 6.
True
500
Write the contrapositive of "If Marias birthday is February 29, then her bday is in a leap year" and find the truth value.
If Maria was not born in a leap year, then her birthday is not February 29. True
500
Can we make a conjecture from the given information? Given: If you leave your car lights on overnight, then your car battery will drain. If you battery is drained, you car might not start.
If you leave your car lights on overnight, then your car might not start.
500
Write the definition as a biconditional: If a lunar eclipse occurs, then the Earth is between the Sun and the Moon.
A lunar eclipse occurs if and only if the Earth is between the Sun and the Moon.
500
Fill in the blanks to complete the two-column proof. Given: TU congruent to UV Prove: SU + TU = SV Statements Reasons TU congruent to UV a. ? b. ? Def of congruent segs. c. ? Seg. Add. Post. SU + TU = SV d. ?
a. Given b. TU = UV c. SU + UV = SV d. Substitution
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