Math Humor Customer: How much are two eggs? Waitress: $1.75 Customer: How much is one egg? Waitress: $1.50 Customer: Then I’ll have the other one.

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Presentation transcript:

Math Humor Customer: How much are two eggs? Waitress: $1.75 Customer: How much is one egg? Waitress: $1.50 Customer: Then I’ll have the other one.

Use properties of equality and congruence to write Algebraic proofs. LT 2.5: Use properties of equality and congruence to write Algebraic proofs.

Today we are going to prove that 1=2 as we learn how to write an Algebraic proof. Hopefully you know that 1≠2 which means there is a logical mistake. See if you can figure out what the mistake is.

Justifications in an Algebraic Proof. What we write: What is means:

Solve each equation. Write a justification for each step. Statements Reasons y + 1 = 5

Solve each equation. Write a justification for each step. Statements Reasons

Solve each equation. Write a justification for each step. Statements Reasons 0 = 2(r – 3) + 4

Write a justification for each step. Statements Reasons

Given that a=b, prove 1=2 Statements Reasons a=b b=a ab = a2 ab - b2 = a2 - b2 b(a-b) = (a+b)(a-b) b=a+b b = 2b 1=2 Can YOU figure out what is wrong with this proof???

Identify the property that justifies each statement. 9) 10) 11) 12)

Statements Reasons

Before you leave… A B C