Download 2-3: Biconditionals and Definitions Biconditional __________________

2-3: Biconditionals and
Definitions
Biconditional
Single true statement
 Combines a __________________
true conditional and its _____
true
___________.
converse
 Join parts of conditionals with ______________.
if and only if

◦ Abbreviated iff.

Symbols
→
→
◦ Combines _________and
__________
↔
◦ Written ____________.
◦ Said “p if and only if q”
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Writing a Biconditional
If the sum of the measures of two angles is 90°, then
the angles are complementary.
True
1. Is the conditional true?
2. What
is the converse and is it true?
True
If two angles are complementary, then the sum of
their measures is 90°.
3. Rewrite
as a biconditional.
The sum of the measures of two angles is 90°if and
only if the angles are complementary.
Identifying Conditionals in Biconditionals
What are the two conditionals that form this biconditional?
Two numbers are additive inverses if and only if their sum is 0
p: two numbers are additive inverses
Conditional
q: their sum is 0
→
If _________________________,
two numbers are additive inverses then __________.
their sum is 0
Converse
→
If two
________________,
numbers sum is 0 then ___________________.
they are additive inverses
2
Components of Good Definitions
1.
Uses clearly understood terms.
◦ Commonly understood or previously defined.
2.
Is precise.
◦
3.
Avoid words such as: large, sort of and almost.
Is reversible.
◦
Can be written as a true biconditional.
Can this definition of an equilateral triangle be written as a
true biconditional?
An equilateral triangle is a triangle with 3 congruent sides.
Conditional
If _________________,
a triangle is equilateral then __________________.
it has 3 congruent sides
Converse
If a_______________________,
triangle has 3 congruent sides then ______________
it is an equilateral
______.
triangle
Biconditional
A triangle is an equilateral triangle if and only if it has 3
congruent sides.
3
Homework: p.101 #
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