Math Humor Q: How is a geometry classroom like the United Nations?

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

LT 2.3: Using Deductive Reasoning to Verify Conjectures

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

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.

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.

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.

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

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 2004 World Series. Conjecture: The Red Sox won the 2004 World Series.

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

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.

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.

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°.