geometry chapter 2 deductive reasoning pages 80-123
TRANSCRIPT
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GEOMETRY CHAPTER 2Deductive Reasoning pages 80-123
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2-1 CONDITIONAL STATEMENTS
• GOAL: Recognize conditional statements
• GOAL: write the converse of conditional statements
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VOCABULARY
• Conditional Statement
• Hypothesis
• Conclusion
• Converse
• Truth Value
• Deductive Reasoning
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CONDITIONAL STATEMENT
• Contains if, then
• Has two parts
• If B is between A and C, then AB +BC = AC.
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HYPOTHESIS
• The part following “IF” • If B is between A and C, then
AB +BC = AC.
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CONCLUSION
• The part following then • If B is between A and C, then
AB +BC = AC.
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CONVERSE
• switch the hypothesis and the conclusion
• If AB + BC = AC, then B is between A and C.
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TRUTH VALUE
• Whether a statement is true or false
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DEDUCTIVE REASONING
• Conclusion based on statements
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FOCUSING QUESTIONING
• IF A ANGLE IS A RIGHT, THEN IT’S MEASURE IS 90 DEGREES.
– Identify the hypothesis– Identify the conclusion– State the converse
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FOCUSING QUESTIONINGANSWER
• IF AN ANGLE IS A RIGHT, THEN IT’S MEASURE IS 90 DEGREES.
– Hypothesis: AN ANGLE IS RIGHT– Conclusion: IT’S MEASURE IS 90 DEGREES– State the converse: IF AN ANGLE’S
MEASURE IS 90 DEGREES, THEN THE ANGLE IS RIGHT
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2-2 BICONDITIONALS AND DEFINITIONS
• Standard: Write biconditionals
• Standard: Recognize good definitions
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VOCABULARY
• Biconditional
• Converse
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BICONDITIONAL
• Contains “if and only if”
• A conditional and converse combined together
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FOCUSING QUESTION
• IF THREE POINTS LIE ON THE SAME LINE, THEN THE POINTS ARE COLLINEAR.
– Identify the hypothesis– Identify the conclusion– State the converse– State a biconditional
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2-4 REASONING IN ALGEBRA
• Standard: Connect reasoning in Algebra and Geometry
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VOCABULARY
• Addition Property
• Subtraction Property
• Multiplication Property
• Division Property
• Reflexive Property
• Symmetric Property
• Transitive Property
• Substitution Property
• Distributive Property
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Addition PROPERTY
• when you add the same number to both sides
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SUBTRACTION PROPERTY
• when you subtract the same number from both sides
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MULTIPLICATION PROPERTY
• When you multiply each side of the equation by the same number
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DIVISION PROPERTY
• When you divide both sides of the equation by the same number
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REFLEXIVE PROPERTY
• the equals sign is like a mirror
• a = a
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SYMMETRIC PROPERTY
• You can change the order
• x = 5 or 5 = x
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TRANSITIVE PROPERTY
• If a = b and b = c, then a = c
• You can take out what looks alike
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SUBSTITUTION PROPERTY
• When you replace
• a = b, then a + c = d or b + c = d
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DISTRIBUTIVE PROPERTY
• Multiply what’s on the outside of the parenthesis with everything on the inside of the parenthesis
• 5(2 + 5) = 10 + 25
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FOCUSING QUESTION
• What are vertical angles?
• What are adjacent angles?
• What are complementary angles?
• What are supplementary angles?
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2.5 PROVE ANGLES CONGRUENT• Standard: Prove and apply
theorems about angles.
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VOCABULARY
• Vertical Angles
• Supplements
• Complements
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Vertical Angles
• Congruent• Directly
across from each other
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COMPLEMENTS
• Equal 90 degrees
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SUPPLEMENTS• Equal 180
degrees