1. Conditional Statements

2. If-Then Statements Contain
2 parts:
The “If” Part:
Hypotheses
If you want your driver’s license,
then you have to pass a computer test.
The “Then” Part: Conclusion

3. If-Then Statements
All teachers at CAT-Pickering are at least 21 years old.
Write the above as a conditional statement.
If you are a teacher at CAT-Pickering, then you are at least 21 years old.

4. If-Then Statements If two angles are congruent,
Write a conclusion to this hypotheses…..
then their measures are equal.

5. Vertical angles are formed if two lines intersect.
What is the hypothesis?
If two lines intersect
Then vertical angles are formed.
What is the conclusion?

6. The “Then” Part: Conclusion
The “If” Part:
Hypotheses
If you get a Red Rider BB gun for Christmas,
then you’ll shoot your eye out.
The “Then” Part: Conclusion

7. A statement that proves the converse false is a
Is the Converse True?
Converse: If you shoot your eye out, you will get a Red Rider BB gun for Christmas.
A statement that proves the converse false is a
counterexample.

8. I shot my eye out, and I did NOT get a Red Rider BB gun for Christmas.
Converse: If you shoot your eye out, you will get a Red Rider BB gun for Christmas.
Here’s a
Counterexample:
I shot my eye out, and I did NOT get a Red Rider BB gun for Christmas.

9. Law of Syllogism If p then q. If q then r. If p, then r.
If I get an A in geometry this marking period, then my mom is happy.
If my mom is happy, she buys me a Lamborghini.

10. Law of Syllogism
If I get an A in geometry this marking period, then …….
My mom buys me a Lamborghini.

11. Law of Syllogism: You can Skip the Middle Statement
If I get an A in geometry this marking period, then my mom is happy.
If my mom is happy, then she buys me a Lamborghini.
If I get an A in geometry this marking period, then my mom buys me a Lamborghini.

12. Another Syllogism…

13. Geometry Cribs…

14. IF You Are Bill Gates, Then You Have Megabucks.
Net Worth =
$ 40 Billion

15. IF You Have Megabucks, Then You Own A Nice House.

16. IF You Are Bill Gates, Then You Own A Nice House.
Medina, Wash.
Gates' 66,000-square-foot compound is built into a hillside on the edge of Lake Washington, near Seattle. Out-of-shape visitors can skip the 84-step hike to the ground floor and opt for an elevator ride instead. Among its enviable amenities: a 60-foot swimming pool with an underwater music system, a 2,500-square-foot gym and a 1,000-square-foot dining room, which seats 24.

17. Law of Detachment I will cancel my wedding. If p then q. P is true.
So, q must be true.
Law of Detachment
If it rains, I will cancel my wedding.
It is raining.
I will cancel my wedding.

18. Because you reach a conclusion from known facts, you use…..

19. Deductive Reasoning

20. Now try some problems on your own.