In today’s geometry lesson, you’re going to learn all about conditional statements!
Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)
We’re going to walk through several examples to ensure you know what you’re doing.
In addition, this lesson will prepare you for deductive reasoning and two column proofs later on.
To better understand deductive reasoning, we must first learn about conditional statements.
A conditional statement has two parts: hypothesis (if) and conclusion (then).
In fact, conditional statements are nothing more than “If-Then” statements!
Sometimes a picture helps form our hypothesis or conclusion. Therefore, we sometimes use Venn Diagrams to visually represent our findings and aid us in creating conditional statements.
But to verify statements are correct, we take a deeper look at our if-then statements. This is why we form the converse, inverse, and contrapositive of our conditional statements.
Well, the converse is when we switch or interchange our hypothesis and conclusion.
Conditional Statement: “If today is Wednesday, then yesterday was Tuesday.”
Hypothesis: “If today is Wednesday” so our conclusion must follow “Then yesterday was Tuesday.”
So the converse is found by rearranging the hypothesis and conclusion, as Math Planet accurately states.
Converse: “If yesterday was Tuesday, then today is Wednesday.”
Now the inverse of an If-Then statement is found by negating (making negative) both the hypothesis and conclusion of the conditional statement.
So using our current conditional statement, “If today is Wednesday, then yesterday was Tuesday”.
Inverse: “If today is not Wednesday, then yesterday was not Tuesday.”
And the contrapositive is formed by interchanging the hypothesis and conclusion and then negating both.
Contrapositive: “If yesterday was not Tuesday, then today is not Wednesday”
A statement written in “if and only if” form combines a reversible statement and its true converse. In other words the conditional statement and converse are both true.
Continuing with our initial condition, “If today is Wednesday, then yesterday was Tuesday.”
Biconditional: “Today is Wednesday if and only if yesterday was Tuesday.”
Examples of Conditional Statements
In the video below we will look at several harder examples of how to form a proper statement, converse, inverse, and contrapositive. And here’s a big hint…
Whenever you see “con” that means you switch! It’s like being a con-artist!
Moreover, we will detail the process for coming up with reasons for our conclusions using known postulates. We will review the ten postulates that we have learned so far, and add a few more problems dealing with perpendicular lines, planes, and perpendicular bisectors.
After this lesson, we will be ready to tackle deductive reasoning head-on, and feel confident as we march onward toward learning two-column proofs!
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