Conditional Statements
Inductive or Deductive
Complementary & Supplementary Angles
Counterexamples
Other Angle Pairs
100
Write the converse of the statement "If I win, then you lose."
What is "If you lose, then I win."
100
Is this inductive or deductive reasoning? Explain. (Must have BOTH the answer and the justification correct to earn points.)
Mrs. Bounds has worn jeans on Friday for the last 3 weeks. Today is Friday. Therefore, Mrs. Bounds will be wearing jeans.
Inductive
It is based on a pattern observed from several cases.
100
What is the complement of 25 degrees?
65 degrees
100
Provide a counterexample:
If you are eating a red fruit, then you are eating an apple.
pomegranate, strawberry, raspberry, cherry, etc
100
Two angles form a linear pair.
One angle is 100 degrees.
What is the other angle?
80 degrees
The linear pair theorem states that if two angles form a linear pair, then they are supplementary (add to 180).
200
Write the contrapositive of the statement "If a shape is a six-sided polygon, then it is a hexagon."
What is: If it is not a hexagon, then a shape is not a six-sided polygon.
200
Which type of reasoning uses postulates, theorems and definitions paired with rules of logic.
Deductive Reasoning
200
Two angles are supplementary. One angle is 7x and the other is 3x. What is x?
7x+3x=180
10x=180
x = 18
200
Provide a counterexample
If 𝑥 + 4 > 10, then x is greater than 8.
6.1, 6.5, 7, 7.3, 7.555555, 7.9999
200
Two angles are vertical angles.
One angle is 5x+10 and the other is 40.
What is x?
5x+10=40
5x=30
x=6
The Vertical Angles Theorem states that vertical angles are congruent.
300
Write the inverse of the statement:
"If they make me run the pacer, then I will try to break my ankle before it starts."
If they don't make me run the pacer, I will not try to break my ankle before it starts.
300
Which type of logic looks at specific cases and finds patterns to draw conclusions?
Inductive Reasoning
300
Two angles are supplementary. Once angle is 11x+20 and the other is 9x+20. What is x?
11x+20+9x+20=180
20x+40=180
20x=140
x=7
300
tea with honey
300
Two angles form a linear pair.
One angle is 3x+10 and the other angle is 2x+40.
What is x?
If two angles form a linear pair, then they are supplementary, according to the Linear Pair Theorem.
3x+10+2x+40=180
5x+50=180
5x=130
x=26
400
Write the definition of right angle as a biconditional.
An angle is a right angle if and only if its measure is 90 degrees.
400
What type of logic is used in geometric proofs?
Deductive Reasoning
400
Two angles are complementary.
One angle is 2x +10 and the other is 3x more than the first angle.
What is x?
2x+10+3x=90
5x+10=90
5x=80
x=16
400
Provide a counterexample to prove the following statement false.
All numbers greater than 20 are divisible by itself, 1, and at least 2 other number.
Any prime number greater than 20
400
Two angles form a linear pair.
One angle is 3x-10 and the other is 6x+46.
What is are the measures of both angles?
If two angles form a linear pair, then they are supplementary.
3x-10+6x+46=180
9x+36=180
9x=144
x=16 so the angles are 38 degrees and 142 degrees.
3*16-10=38
6*16+46=142
500
The Vertical Angles Theorem says
"If two angles are vertical angles, then they are congruent."
Consider the converse, inverse, & contrapositive.
Can this be written as a valid biconditional? Explain your reasoning. (Must have correct reasoning to earn the points!!!)
Two angles are vertical angles if and only if they are congruent.
NOT VALID
"If two angles are vertical angles, then they are congruent." is a true statement. The converse "If two angles are congruent, then they are vertical angles." is false. ALL FOUR logical statements must be true for the biconditional to be valid.
500
Angles 1 & 2 form a linear pair. It's given that angle 1 is 50 degrees. If angles form a linear pair, then they sum to 180 degrees, according to the linear pair theorem. So angle 1 + angle 2 = 180. By substitution, 50 + angle 2 = 180. Using the subtraction property of equality, angle 2 must be 130 degrees.
Is the explanation above an example of inductive or deductive reasoning? Explain. (Must have BOTH the answer and the justification correct to earn points.)
Deductive Reasoning
The laws of logic are being used and each statement is backed up by a theorem of property. It is NOT a pattern based on several specific cases.
500
Two angles are supplementary. One angle is 45 less than twice the measure of the other angle. What are measures of both angles?
x+2x-45=180
3x-45=180
3x=225
x=75
The two angles are 75 degrees and 105 degrees.
500
Provide a counterexample to prove the following statement false.
The sum of two numbers is always more than the greater number.
Counter example: -2 + -3 = -5
500
Two angles are vertical angles.
One angle is 45+4x+12x and the other is 6x+50+55.
What is x?
45+4x+12x=6x+50+55
45+16x=6x+105
45+10x=105
10x=60
x=6
6*6+50+55=141
The measure of the both angles is 141 degrees.