Conditional Statements in Geometry

Conditional statements in geometry can be confusing for even the best geometry students. The logic and proof portion of your geometry curriculum is bursting with new terminology! There are conditional statements, and the inverse, converse, contrapositive, etc. And wait, we represent them with p’s and q’s?! Ok, let’s break it down. 

What is a Conditional Statement?

A conditional statement in geometry is an “if-then” statement.

The part of the statement that follows “if” is called the hypothesis, and the part of the statement that follows “then” is called the conclusion.

We also represent conditional statements symbolically. For a conditional statement, p represents the hypothesis and q represents the conclusion. Symbolically we write p → q, which reads “if p then q.”

Statements Related to the Conditional Statement

 Inverse. To write the inverse of the conditional statement, you negate the hypothesis AND conclusion. Symbolically, it’s written as ~p → ~q and read as “If not p, then not q”.

Converse. To write the converse of the conditional statement, you switch the hypothesis and conclusion. Symbolically, it’s written as q → p and read “if q then p”.

Contrapositive. To write the contrapositive of the conditional statement, you both negate AND switch the hypothesis and conclusion. Symbolically, it’s written as ~q → ~p and read “if not q, then not p”. 

Resources for Teaching Conditional Statements

Looking for a graphic organizer to summarize conditional statements in geometry? Leave me your e-mail and I’ll send you one for FREE!  

Students can practice writing statements and determining their truth value with this self-checking assignment

Stay tuned for a Logic and Proof Unit Bundle coming soon! 

Happy teaching!

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