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Using Deductive Reasoning 2-3 to Verify Conjectures Warm-Up = 2 points / +2 if you have it correct when I come by / -2 if you’re not working on it Holt McDougal Geometry Using Deductive Reasoning 2-3 to Verify Conjectures 20 Point Quiz ---- Due 10/23/15 Write the converse, inverse, and contrapositive of the conditional statement. Use the Science Fact to find the truth value of each. If an animal is an adult insect, then it has six legs. Holt McDougal Geometry Using Deductive Reasoning 2-3 to Verify Conjectures Deductive reasoning is the process of using logic to draw conclusions from given facts, definitions, and properties. Deductive reasoning = conclusions from DATA. Inductive reasoning = conclusions from patterns. Holt McDougal Geometry Using Deductive Reasoning 2-3 to Verify Conjectures Example 1B: Media Application Is the conclusion a result of inductive or deductive reasoning? There is a myth that the Great Wall of China is the only man-made object visible from the Moon. The Great Wall is barely visible in photographs taken from 180 miles above Earth. The Moon is about 237,000 miles from Earth. Therefore, the myth cannot be true. The conclusion is based on logical reasoning from scientific research. It is a result of deductive reasoning. Holt McDougal Geometry Using Deductive Reasoning 2-3 to Verify Conjectures Determine if the conjecture is valid Given: If the side lengths of a triangle are 5 cm, 12 cm, and 13 cm, then the area of the triangle is 30 cm2. The area of ∆PQR is 30 cm2. Conjecture: The side lengths of ∆PQR are 5cm, 12 cm, and 13 cm. Holt McDougal Geometry Using Deductive Reasoning 2-3 to Verify Conjectures Example 2B: Verifying Conjectures by Using the Law of Detachment 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. Holt McDougal Geometry Using Deductive Reasoning 2-3 to Verify Conjectures Check It Out! Example 2 Determine if the conjecture is valid by the Law of Detachment. Given: If a student passes his classes, the student is eligible to play sports. Ramon passed his classes. Conjecture: Ramon is eligible to play sports. Holt McDougal Geometry Using Deductive Reasoning 2-3 to Verify Conjectures Another valid form of deductive reasoning is the Law of Syllogism. It allows you to draw conclusions from two conditional statements when the conclusion of one is the hypothesis of the other. Law of Syllogism If p q and q r are true statements, then p r is a true statement. Holt McDougal Geometry Using Deductive Reasoning 2-3 to Verify Conjectures Example 3A: Verifying Conjectures by Using the Law of Syllogism Determine if the conjecture is valid by the Law of Syllogism. Given: If a figure is a kite, then it is a quadrilateral. If a figure is a quadrilateral, then it is a polygon. Conjecture: If a figure is a kite, then it is a polygon. Holt McDougal Geometry Using Deductive Reasoning 2-3 to Verify Conjectures Example 3B: Verifying Conjectures by Using the Law of Syllogism Determine if the conjecture is valid by the Law of Syllogism. Given: If a number is divisible by 2, then it is even. If a number is even, then it is an integer. Conjecture: If a number is an integer, then it is divisible by 2. Holt McDougal Geometry Using Deductive Reasoning 2-3 to Verify Conjectures Check It Out! Example 3 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. Holt McDougal Geometry Using Deductive Reasoning 2-3 to Verify Conjectures Example 4: Applying the Laws of Deductive Reasoning Draw a conclusion from the given information. A. Given: If 2y = 4, then z = –1. If x + 3 = 12, then 2y = 4. x + 3 = 12 B. 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. mA= 135°, and mB= 45°. Holt McDougal Geometry