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Published byMabel McGee Modified over 9 years ago
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I can’t wait to see how well I did on my test!
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Lesson 2-1 I can make an educated guess based on reasoning I can find counterexamples I can use algebra to write 2- column proofs
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An educated guess based on known information
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∠ABC ≅ ∠DBE A B C D E Conjecture:
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N P Q NP≅ PQ Conjecture:
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An example that shows a conjecture is false. Only need one
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False! 5 2 = 10
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False! Counterexample: 1 2
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True!
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False! Counterexample: A B C D E F
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logical argument supported true
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a = a 5 = 5 if a = b then b = a if 5 = x then x = 5
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if a = b and b = c then a = c if x = 5 and 5 = y, then x = y
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if a = b then a + c = b + c if x + -3 = 8 then x + -3 + 3= 8 + 3
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if a = b then a – c = b – c if x + 10 = 15 then x + 10 – 10 = 15 – 10
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if a = b then ac = bc if x = 10 3 then 3(x) = 10(3) 3
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if a = b then a = b c if 2x = 10 then 2 2 2x = 10
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if a = b then a can be replaced by b if x = 3 then 2x + 1 = 2(3) + 1
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a(b + c) = ab + ac 2(x + 5) = 2x + 10
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statementsreasons the steps properties that justify your steps
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1. 3x + 5 = 171. Given 2. 3x + 5 – 5 = 17 – 5 2. Subtraction prop. 3. 3x = 123. Substitution 4. 3x/3 = 12/34. Division prop. 5. x = 45. Substitution
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1. 6x – 3 = 4x + 11. Given 2. 6x – 4x – 3 = 4x – 4x + 1 2. Subtraction prop. 3. 2x – 3 = 13. Substitution 4. 2x – 3 + 3 = 1 + 34. Addition prop. 5. 2x = 45. Substitution 6. 2x/2 = 4/26. Division prop. 7. x = 27. Substitution
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ASSIGNMENT: 2-1 worksheet, both sides!
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