1. Math Humor Q: How is a geometry classroom like the United Nations?
A: They both have lots of rulers!

2. LT 2.3: Using Deductive Reasoning to Verify Conjectures

4. Example 1
Is the conclusion a result of inductive or deductive reasoning?
The sum of the angles in a triangle is 180⁰. This polygon is a triangle. The sum of the triangle’s angles is 180⁰

5. Example 2
Is the conclusion a result of inductive or deductive reasoning?
The sum of the angles in a quadrilateral is 180⁰ more than a triangle. The sum of the angles in a pentagon will be 180⁰ more than a quadrilateral.

6. Example 3
Is the conclusion a result of inductive or deductive reasoning?
It has rained every day for the past two weeks. It will rain tomorrow.

7. Example 4
Is the conclusion a result of inductive or deductive reasoning?
All ducks have webbed feet. I see a duck in the pond. The duck has webbed feet.

8. Law of Detachment
If is a true statement and p is true, then q is true.

9. Example 5
Determine if the conjecture is valid by the Law of Detachment.
Given: In the World Series, if a team wins four games, then the team wins the series. The Red Sox won four games in the World Series.
Conjecture: The Red Sox won the World Series.

10. Law of Syllogism
If and are true statements, then is a true statement.

11. Example 6
Determine if the conjecture is valid by the Law of Syllogism.
Given: If an animal is a mammal, then it has hair. If an animal is a dog, then it is a mammal.
Conjecture: If an animal is a dog, then it has hair.

12. Example 7 Draw a conclusion from the given information.
Given: If a polygon is a triangle, then it has three sides. If a polygon has three sides, then it is not a quadrilateral. Polygon P is a triangle.

13. Example 8 Draw a conclusion from the given information.
If the sum of the measures of two angles is 180°, then the angles are supplementary If two angles are supplementary, they are not angles of a triangle. mA= 135°, and mB= 45°.