Geometry Notes 2-1
Conditional Statements
A conditional is a ____________________________ statement.
If you listen to your music too loud, then you will lose your hearing.
The ___________________ follows the “if” part. The _______________________ follows the
“then” part.
Example 1 a) Write the following statement as a conditional. b) Identify p and q and write in
symbolic form.
1. My parents are happy when I do well in math
2. Drinking milk makes you strong
Vocabulary and Key Concepts
Statement
Examples
Conditional
If you live in Fort Collins
then you live in Colorado
Symbolic You read the symForm
bolic form as:
p q
If ___ then ___
OR
__ implies ____
q p
Converse
If _____________________
then ________________________
If ___ then _____
OR
__ implies ____
A conditional statement has a _____________________________ of True or False.
To show a conditional statement is False, you must find __________________________.
A converse is the statement which exchanges the ___________________ and
_______________.
Example 2. Write the converse and write true/false. If false provide a counterexample
Show that each conditional is false by finding a counterexample.
1. If it is 12:00 noon, then the sun is shining.
2. If a number is divisible by 3, then it is odd.
3. If you are a twin, then you have a sibling.
Example 3. Venn Diagrams
1. Draw a Venn diagram to illustrate the following conditional. “If my pet is a poodle, then my
pet is a dog.”
2. Write the conditional statement for this Venn
Diagram to the right.
Fruit
apple
Geometry Notes 2-2
Biconditionals and Definitions
When both the conditional and converse are true, they can be combined to form a
_________________________. The words ______________________ join the two parts.
Example 1. Writing a Biconditional:
Conditional: If it has 8 legs then it is a spider.
Converse: If _______________ then ___________________.
If both statements are true then you can replace the words “ ____ “ and “ ______” with
________________ in the middle of the sentence.
Biconditional:
Vocabulary and Key Concepts
Statement
Examples
Biconditional
An angle is a right angle
if and only if the angle is 90o
Symbolic You read the symForm
bolic form as:
____ if and only if
_____
Write the 2 conditional statements that make up the biconditional.
1. An angle is a right angle if and only if the angle is 90o
2. It is Valentine’s Day if and only if it is February 14th.
Example 2. Writing good Definitions
A good definition is ___________________, ___________________, clearly understood terms,
and can be written as a true __________________
Example. A triangle is a polygon with exactly three sides.
Conditional: If a polygon is a triangle then it has three sides.
Converse:
If both statements are ___________ then they can be combined to form a biconditional.
Biconditional: