Inductive Reasoning
Name the next term: 2,4,6,8
10
Make a conjecture:
The product of two even numbers
The product of two even numbers is even
State if the conjecture is true or false, if false make a counter example:
Angle A and angle B are complementary angles, then they share a common side.
False
(Image)
They could be nonadjacent so angle a is 45 degrees and angle b is 45 degrees but that don't share a side.
Identify the hypothesis and conclusion:
If today is Friday, then tomorrow is Saturday.
H: today is Friday
C: tomorrow is Saturday
What is the hypothesis?
The statement after "if"
Name the next term:
2, 22,222,2222
22222
Make a conjecture:
The relationship between a and b if a+b =0
a and b are additive inverses
State if the conjecture is true or false, if false make a counter example:
If a ray intersects a segment at its midpoint, then the ray is perpendicular to the segment.
False
(Image)
One angle could be 20 degrees another could be 140
Write the statement in if-then form:
The measure of an acute angle is between 0 and 90:
If the angle is acute, then its measure is between 0 and 90.
What is a contrapositive?
Swapping and have the opposite meaning
Name the next term:
1,4,9,16
25
Make a conjecture:
The product of two and a number, plus one
The result is odd
State if the conjecture is true or false, if false make a counter example:
If you have three points A, B, and C, then A, B, and C are noncollinear.
False
(image)
All points on the same line
State true or false, if false give counterexample:
If you live in Charlotte, then you live in North Carolina.
False, Michigan
What is a converse?
The hypothesis and conclusion are swapped
Name the next day:
Sunday, Tuesday,Thursday
Saturday
Make a conjecture:
The relationship between line AP and line PB if M is the midpoint of line AB and P is the midpoint of line AM
Line PB is three times as long as line AP
State if the conjecture is true or false, if false make a counter example:
If angle A and angle B are vertical angles, then they are congruent.
True
Write the converse:
All whole numbers are integers
If a number is a whole number, then it is an integer.
What is a conditional statement?
The hypothesis and conclusion
Name the next month:
January, March, May
July
Make a conjecture:
The relationship between the set of points in a plane equidistant from point A.
The set of points in a plane equidistant from point A in a circle
State if the conjecture is true or false, if false make a counter example:
If the area of a rectangle is 20 square meters, then the length is 10 meters and the length is 2 meters
False
The length could be 4m and the width could be 5m
Write the inverse then write true or false, if false state a counterexample:
If a number is divisible by 4, then it is divisible by 2.
If a number is not divisible by 4, then it is not divisible by 2.
False: 6 is not divisible by 4
What is isolating?
Solving for a variable