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Logic Notes: Biconditional Statements
Biconditional statements is a single true statement that combines a true conditional and its true
____________. You can write a Biconditional by ___________ the two parts of each conditional
with the phrase _________________________.
Conditional: If the sum of the measure of two angles is 180, then the two angles are
supplementary.
_______: If two angles are supplementary, then the sum of the measures of the two angles is 180.
Biconditional Statement: Two angles are supplementary if and only if the sum of the measures of
the two angles is 180.
***Statements that can be written as biconditional statements are ________________***
For #1-5 write the converse of each statement. Determine if each statement is true or false. If both the
conditional and converse statements are true re-write them as a biconditional statement. If the statement is
false write a counterexample.
Ex 1) If two segments have the same length, then they are congruent.
Converse:
Biconditional/counterexample:
Ex 2) If a number is divisible by 20, then it is even.
Converse:
Biconditional/counterexample:
Ex 3) If an angle is 90 degrees, then it is a right angle.
Converse:
Biconditional/counterexample:
Ex 4) If a quadrilateral is a trapezoid, then it has only one pair of parallel sides.
Converse:
Biconditional/counterexample:
Ex 5) If a polygon is a square, then it has four congruent sides.
Converse:
Biconditional/counterexample:
Write 2 conditional statements that you can write as biconditional statements then rewrite it as a biconditional
statement.
Statement #1: ___________________________________________________________________________
_________________________________________________________________________________________
Biconditional Statement: __________________________________________________________________
_________________________________________________________________________________________
Statement #2: ___________________________________________________________________________
_________________________________________________________________________________________
Biconditional Statement: __________________________________________________________________
_________________________________________________________________________________________
Ex 6) Which conditional statements form true biconditional statements? (There may be more than one)
A.) If x > 0, then |x| > 0.
B.) If x3 = 125, then x = 5.
C.) If x = 19, then 2x – 3 = 35.
D.) If x = 3, then x2 = 9.
Ex 7) Which of the following is a good definition? (There may be more than one)
A.) Rectangles are quadrilaterals with four right angles.
B.) A fish is an animal that swims.
C.) A penny is a coin worth one cent.
D.) Giraffes are animals with very long necks.
Ex 8) Which of the following is a good definition? (There may be more than one)
A.) A line bisectors intersects a segment only at its midpoint.
B.) An integer is divisible by 100 if its last two digits are zeroes.
C.) An acute angle is an angle that is less than 90.
D.) An isosceles triangle is a polygon with at least 2 congruent sides.