Geometry: Conditional Statements III - Converse, Inverse, Contrapositives

Are you introducing formal logic to your class and having trouble coming up with additional examples? Are you teaching logic for the first time and struggling with how to explain things to your class? This activity is great for the students and also for the teachers.

This is my third variation for conditional statements available on TpT and is the one is comes with two printable versions after reading the suggestions on my other products.

Version 1- This version is simply a 1-page document with 20 statements on it. The advantage of using this would be that it is easy to copy and simple to look it. The only downside is that the students would have to write out the statements in their notebooks. (Hint: If they type their answers they can copy and paste and add the word NOT for at least half of the sentences so it is a little quicker than hand-writing the entire thing.)

Version 2 - This version is set up like a table and is easier to read and it might be helpful for struggling students. The only disadvantage to this is that it would take more paper and more time to copy.

Both versions are included in this download.


For this assignment the students will have to come up with the converse, inverse and contrapositive of each statement and also determine their truth value. If they are false they must provide a counter-example.

These are more fun that what is usually in the math textbooks because these statements do not all involve math. I have found that using math statements to introduce this topic make everything much more difficult to understand. The students like these because they get to be creative in their counter-examples. Here is an example of the types of statements that are listed.

Conditional: If you are a human being then you have ears.
The students then will write:
Converse: If you have ears then you are a human.
Inverse: If you are not a human being then you do not have ears.
Contrapositive: If you do not have ears then you are not a human being.

In this case the truth values would be: True, False, False, True.

My worksheet gives all of the answers and also explains what a good counter-example would be.

**Teaching Tip: If you look at the example above some students might say "I think the first statement is false because maybe a human had their ears chopped off." It is up to you if you want to let the kids think up these extreme examples. On one hand it can be fun and interesting to include them but then they sometimes miss the simple idea we are trying to get them to learn. I have taught it both ways and personally prefer that they don't get too carried away with their counter-examples because it tends to confuse them on the tests and they over think everything.

Another tip is that this entire packet might be a little too long for one homework assignment. You may want to assign a few a night or give them time in class to work on it.

I have plenty of other geometry resources so please contact me if you are looking for something particular. Also, check out my other listings. If you are pleased with this download I would appreciate any feedback you would be willing to leave.

Thanks and happy teaching!


Conditional Statements III by Dana Burrows McCaskey is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.