I can’t wait to see how well I did on my test!. Lesson 2-1 I can make an educated guess based on reasoning I can find counterexamples I can use algebra.

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Presentation transcript:

I can’t wait to see how well I did on my test!

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

An educated guess based on known information

∠ABC ≅ ∠DBE A B C D E Conjecture:

N P Q NP≅ PQ Conjecture:

An example that shows a conjecture is false. Only need one

False! 5 2 = 10

False! Counterexample: 1 2

True!

False! Counterexample: A B C D E F

logical argument supported true

a = a 5 = 5 if a = b then b = a if 5 = x then x = 5

if a = b and b = c then a = c if x = 5 and 5 = y, then x = y

if a = b then a + c = b + c if x + -3 = 8 then x = 8 + 3

if a = b then a – c = b – c if x + 10 = 15 then x + 10 – 10 = 15 – 10

if a = b then ac = bc if x = 10 3 then 3(x) = 10(3) 3

if a = b then a = b c if 2x = 10 then 2 2 2x = 10

if a = b then a can be replaced by b if x = 3 then 2x + 1 = 2(3) + 1

a(b + c) = ab + ac 2(x + 5) = 2x + 10

statementsreasons the steps properties that justify your steps

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

1. 6x – 3 = 4x Given 2. 6x – 4x – 3 = 4x – 4x Subtraction prop. 3. 2x – 3 = 13. Substitution 4. 2x – = Addition prop. 5. 2x = 45. Substitution 6. 2x/2 = 4/26. Division prop. 7. x = 27. Substitution

ASSIGNMENT: 2-1 worksheet, both sides!