1. Using Properties from Algebra to Prove Statements Section 2.5

2. Essential Question How are algebraic properties used in logical arguments?

3. Add 18 to your birth month Multiply by 25 Subtract 333 Multiply by 8 Subtract 554 Divide by 2 Add your birth date Multiply by 5 Add 692 Multiply by 20 Add only the last two digits of your birth year Subtract 32940 to get your birthday!

5. Multiply the first number of your age by 5. Add 3. Double this figure. Add the second number your age to the figure Deduct 6 and you will have their age.

7. Whenever you solve for a variable you are unknowingly using different algebraic properties. The algebraic properties that we will look at are: ▫Addition Property ▫Subtraction Property ▫Multiplication Property ▫Division Property ▫Substitution Property ▫Distributive Property ▫Reflexive Property ▫Symmetric Property ▫Transitive Property

11. Let’s try one 2x – 5 = x + 12Given 2x = x + 17 Addition Property X = 17Subtraction Property

12. How ‘bout another

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14. Using the properties to prove statements Algebraic proofs require you to solve the problem algebraically and then state the property that allows you to do each step. Proofs that are more geometric require you to do the same thing, but are slightly more abstract.

15. Proving two angles are supplementary. Angle ABC and CBD are a linear pair m ABC + mCBD = 180° Angle ABC and CBD are supplementary Given Def. Linear Pair Def. Supplementary

16. Show that the areas are the same.

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