Name:_____________
Hour:___
2.2: Biconditional Statements
Biconditional:
Symbolic form of “if and only if”:
Write a biconditional statement which would represent each statement below and its
converse.
1) If x=4, then 3x+8=20
2) If an angle is straight, then it measures 180.
3) If two segments are congruent, then they are the same length.
4) If you are a KU fan, then you are a Jayhawk.
Write each of the following biconditional statements as a conditional statement and its
converse.
5) It is a bird if and only if it has feathers.
6) It’s the weekend if and only if it is Saturday.
7) You live in Lawrence if and only if you go to Free State.
Determine whether the biconditional statement is true or false. If false, indicate which
part is false and provide a counterexample.
8) The angle is obtuse if and only if it measures 133.
9) A line is perpendicular if and only if it forms a 90 degree angle.
10) It is a fish if and only if it lives in water.
11) A point divides a segment in to two congruent segments if and only if it is a
midpoint.
What are the three aspects of a definition that make them good definitions?
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Write the conditional, converse and the biconditional of the following words to show it is
reversible.
13) Triangle 
Defintion: a polygon with exactly three sides.
Conditional:
Converse:
Biconditional:
14) Perpendicular Iines
Definition: two lines that intersect to form right angles
Conditional:
Converse:
Biconditional:
Is each statement below a good definition? If not, explain and provide a
counterexample.
15) A cat is an animal with whiskers.
16) A dog is a good pet.
17) A segment is part of a line.
18) Parallel lines do not intersect.
19) A square is a figure with two pairs of parallel sides.
20) An angle bisector is a ray that divides an angle into two congruent angles.