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Unit 3 – Reasoning and Proof
Lesson 3 - Biconditionals and Definitions (p. 75)
Writing Biconditionals
 Biconditional - _____________________________________________________________
– Writing a Biconditional
Consider this true conditional statement. Write its converse. If the converse is also true,
combine the statements as a biconditional.
Conditional: If two angles have the same measure, then the angles are congruent.
Converse:____________________________________________________________
____________________________________________________________________
Use the
Conditional!
Are both the conditional and the converse true?______________ If yes, then write the
biconditional.
Biconditional:_________________________________________________________
_____________________________________________________________________
– Separating a Biconditional into Parts
Write two statements that form this biconditional.
A number is divisible by 3 if and only if the sum of its digits is divisible by three.
Conditional #1:_______________________________________________________
___________________________________________________________________
Conditional #2:_______________________________________________________
____________________________________________________________________
Recognizing Good Definitions




What is a good definition?__________________________________________________
A good definition uses clearly understood terms.
A good definition is precise.
A good definition is reversible.
Lesson 3 - Biconditionals & Definitions
Page 1
Revised Fair 2014-2015
- Writing a Good Definition
Show that this definition of perpendicular lines is reversible. Then write it as a true
biconditional.
Definition: Perpendicular lines are two lines that intersect to form right angles.
Conditional:_____________________________________________________
_______________________________________________________________
Converse:_______________________________________________________
_______________________________________________________________
Are the two conditionals true?___________ If so, write the definition as a biconditional.
Biconditional:____________________________________________________
________________________________________________________________
Real-World Connection
Is the given statement a good definition?
a. An airplane is a vehicle that flies.
b. A triangle has sharp corners.
c. A square is a figure with four right angles.
Statement
Example
Symbolic Form
You Read
Conditional (2-1)
If an angle is a straight
angle, then its measure is
180 .
pq
If p, then q.
Converse (2-1)
If the measure of an angle is
180 , then it is a straight
angle.
q p
If q, then p.
Biconditional (2-2)
An angle is a straight angle
if and only if its measure is
180 .
pq
p if and only if q.
Lesson 3 - Biconditionals & Definitions
Page 2
Revised Fair 2014-2015