Transcript Biconditionals and Definitions LESSON 2-2 Additional Examples Consider this true conditional statement. Write its converse.

Biconditionals and Definitions
LESSON 2-2
Additional Examples
Consider this true conditional statement. Write its
converse. If the converse is also true, combine the
statements as a biconditional.
Conditional: If x = 5, then x + 15 = 20.
To write the converse, exchange the hypothesis and conclusion.
Converse: If x + 15 = 20, then x = 5.
When you subtract 15 from each side to solve the equation, you get
x = 5. Because both the conditional and its converse are true, you can
combine them in a true biconditional using the phrase if and only if.
Biconditional: x = 5 if and only if x + 15 = 20.
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GEOMETRY
Biconditionals and Definitions
LESSON 2-2
Additional Examples
Write the two statements that form this biconditional.
Biconditional: Lines are skew if and only if they are noncoplanar.
A biconditional is written as two conditionals that are converses of
each other.
Conditional: If lines are skew, then they are noncoplanar.
Converse: If lines are noncoplanar, then they are skew.
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GEOMETRY
Biconditionals and Definitions
LESSON 2-2
Additional Examples
Show that this definition of triangle is reversible.
Then write it as a true biconditional.
Definition: A triangle is a polygon with exactly three sides.
The original conditional is true.
Conditional: If a polygon is a triangle, then it has exactly three sides.
The converse is also true.
Converse: If a polygon has exactly three sides, then it is a triangle.
Because both statements are true, they can be combined to form a
biconditional. A polygon is a triangle if and only if it has exactly three
sides.
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GEOMETRY
Biconditionals and Definitions
LESSON 2-2
Additional Examples
Is the following statement a good definition? Explain.
An apple is a fruit that contains seeds.
The statement is true as a description of an apple.
Now exchange “An apple” and “a fruit that contains seeds,” and the
reverse reads: A fruit that contains seeds is an apple.
There are many other fruits containing seeds that are not apples, such
as lemons and peaches. These are counterexamples, so the reverse
of the statement is false.
The original statement is not a good definition because the statement
is not reversible.
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GEOMETRY