1. Do Now:
True
2. False
3. False C D

2. Lesson 2-4: Deductive Reasoning
Goal: Use the Law of Detachment and the law of Syllogism.

3. Laws of Logic: Law of Detachment:
If the hypothesis of a true if-then statement is true, then the conclusion is also true.
Ex: If you are late for your interview, you will probably not be offered the job You are late for your interview.
By the Law of Detachment we can conclude that you will probably not be offered the job.

4. Example 1: Using the Law of Detachment.
What can you conclude from the given true statements?
If a student gets and A on a final exam, then the student will pass the course.
Felicia got an A on her history final.
If a ray divides an angle into two congruent angles, then the ray is an angle bisector.
𝑅𝑆 divides ∠𝐴𝑅𝐵 so that ∠𝐴𝑅𝑆=∠𝑆𝑅𝐵
If two angles are adjacent, then they share a common vertex.
∠1 𝑎𝑛𝑑 ∠2 share a common vertex.

5. Laws of Logic: Law of Syllogism: If statement p, then statement q.
If statement q, then statement r.
If statement p, then statement r.
Ex: If Naomi saves enough money, she can buy a concert ticket If she buys a concert ticket, she can see her favorite band.
So it follows from the Law of Syllogism that If Naomi saves enough money, she can see her favorite band.
If these statements are true,
then this statement is true.

6. Example 2: Using the Law of Syllogism
What can you conclude from the given information?
A) If a figure is a square, then the figure is a rectangle.
If a figure is a rectangle, then the figure has four sides.
If a figure is a square, then the figure has four sides.
B) If you do gymnastics, then you are flexible.
If you do ballet, then you are flexible.

7. Example 3: Using the Laws of Syllogism and Detachment.
What can you conclude from the given information?
If you live in Cincinnati, then you live in Ohio.
If you live in Ohio, then you live in the United States.
Ken lives in Cincinnati.
Ken Lives in the United States

8. Checkpoint:
The midpoint of 𝐴𝐵 is at (2, 0).

9. Checkpoint:
If the perimeter of a square is 20 feet, then the area is 25 square feet.

10. Assignment:
Pp 110 – 112 #’s 6 – 32 even