If-Then Form
Counter-
Example
Converse
biconditionals
Definition
100

Tenth graders are in Geometry.

What is "If you are a tenth grader, then you are in Geometry."

100

If a number squared is 9 then the number must be 3.

What is "The number could be -3"

100

If the child is 5 years old, then they are in kindergarden.

What is "If a child is in kindergarden, then they are 5 years old"

100
The two statements: If you are on the tennis team, then you like tennis. If you like tennis, then you are on the tennis team. can be formed into the biconditional
What is "You are on the tennis team,iff, you like tennis"
100
The statements: "A polygon with 3 sides is a triangle." and "A triangle is a polygon with 3 sides." can be formed into this single definition in "if and only if" form.
What is "A polygon has 3 sides, if and only if, it is a triangle."
200
Puppies are small.
What is "If an animal* is a puppy, then it is small" *answers may vary for this
200
Geometry students never bring bagels in for the class on Mondays.
What is "Students may bring bagels in August 21" (NOTE: STUDENTS MUST BRING IN BAGELS TO RECEIVE CREDIT FOR THIS QUESTION)
200
If there is snow on the ground, flowers are not in bloom.
What is "If flowers are not in bloom, then there is snow on the ground."
200
The two statements: If x is odd, then 2x is even. If 2x is even, then x is odd. can be formed into the biconditional
What is "x is odd, iff, 2x is even."
200
The statements: "If a number is divisible by 10 then it ends in 0." and "If a number ends in 0, then it is divisible by 10." can be formed into this single definition in "if and only if" form.
What is "A number is divisible by 10, iff, it ends in 0.
300
A line contains at least 2 points.
What is "If a shape* is a line then it contains at least 2 points." *answers may vary for this
300

What is, "Any three points must lie on a line."

What is Points A, B, C that are not on the same line (must have a picture)

300
If a = b, and b = c, then a = c.
What is "If a = c, the a = b, and b = c."
300

The biconditional statement: You get an A, iff, your grade is at least a 90%. Can be separated into these two conditional statements.

What is "If you get an A, then your grade is at least a 90%." and "If you get at least a 90% then you get an A."

300

The statement, "A tiger is a mammal." is a bad definition because...

What is the converse, " If an animal is a mammal then it is a tiger." is false.

400
A plane contains at least 3 collinear points
What is "If a shape* is a plane, then it contains 3 collinear points." *answers may vary for this
400
If points are coplanar, then they are collinear.
What is "Points A,B, and C that are on the same plane but not the same line" (must have a picture)
400
If 2 points lie on a plane, then the line containing them lies in the plane.
What is "if a line containing 2 points lies in a plane, then the two points lie on the plane"
400
The biconditional statement: "A shape is a square, iff, it is regular." Can be separated into these two conditional statements.
What is "If a shape is a square then, it is regular." and "If a shape is regular, then it is a square."
400
The statement, "All geometry students are students." is a bad definition because...
What is the converse, "If a person is a student, then he or she is a geometry student is false."
500
Midpoints divide a segment into two congruent segments.
What is, " If a point is a midpoint, then it divides a segment into two congruent segments."
500
The square root of any number must be smaller than the original number.
What is " 0, or 1, or any number given between 0 and 1"
500

If a triangle is a right triangle, then c2+b2=c2

If a triangle satisifies c2=b2+a2, then the triangle is a right triangle

500

A line (et. al.) divides an angle into two congruent angles, iff, it divides the angle into two congruent angles.

If a line (et. al.) divides an angle into two smaller angles then it divides the angle into two congruent angle.

If two smaller angles sum to create a bigger angle then the adjacent side is an angle bisector.

500

What is the ending of the statement, two polygons are congruent, iff...

All angles and sides in one triangle are congruent to the angles and sides of one triangle are to their corresponding sides of the other triangle

M
e
n
u