Geometry
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Unit 2: Reasoning & Proof
Lesson 2.2:
What are Conditional Statements and How Can We Use Them?
"A conditional is an if-then statement."
(Pearson)
(Pearson)
A conditional is written as thus:
if (hypothesis), then (conclusion)
if (hypothesis), then (conclusion)
Consider the following bumper sticker:
A few conditionals I have found to be true in my own experience:
If you complete your homework to the best of your ability, then you will perform better on tests.
If you don't brush your teeth, then you will get cavities.
If you aren't friendly to people, then you find it challenging to make friends.
Can you create a conditional based on your own experience?
Please write it and share it with your partner.
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A truth value can only have two states: true or false.
Let's look at related conditionals.
Let's look at related conditionals.
example:
Consider the following conditional:
If a figure is a square, then the figure is a quadrilateral.
p: A figure is a square.
q: A figure is a quadrilateral.
What is the converse of this statement? The inverse? The contrapositive?
Which are true? Which are false?
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Converse: If a figure is a quadrilateral, then the figure is a square. (false) Inverse: If the figure is not a square, then the figure is not a quadrilateral. (false) Contrapositive: If the figure is not a quadrilateral, then the figure is not a square. (true) |
As you practice the classwork and homework,
pay special attention to the converse.
It will become an important tool of our thinking in the next lesson,
when we learn about biconditionals.
pay special attention to the converse.
It will become an important tool of our thinking in the next lesson,
when we learn about biconditionals.