Algebra 3.4 Algebra Properties mbhaub@mpsaz.org

Geometry 2.4 Reasoning with Algebra Properties Goals Use properties from algebra. Use properties to justify statements. March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Don’t copy all of this down You have had most before. Copy the ones that are new to you You need to have them all memorized. This as well as all presentations are available on-line. March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Addition Property Addition Property If a = b, then a + c = b + c. Example x – 12 = 15 x – 12 + 12 = 15 + 12 x = 27 March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Subtraction Property Subtraction Property If a = b, then a – c = b – c Example x + 30 = 45 x + 30 – 30 = 45 – 30 x = 15 March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Multiplication Property If a = b, then ac = bc Example March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Division Property Division Property Example March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Other Properties Reflexive Property For any number a, a = a. Symmetric Property If a = b, then b = a. Transitive Property If a = b and b = c, then a = c Substitution Property If a = b and a = c, then b = c Distributive Property a(b + c) = ab + ac March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Identify the Property If 43 = x, then x = 43. Property? Symmetric March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Identify the Property If 3x = 12, then 12x = 48 Property? Multiplication March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Identify the Property If x = y, and y = 10, then x = 10 Property? Transitive March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Identify the Property If x = 12, then x + 2 = 14 Property? Addition March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Using a Property Addition Property: If n = 14, then n + 2 = _________ 16 March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Using a Property Symmetric: If AB = CD, then CD = ________ AB March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Using a Property Transitive: If mA = mB, and mB = mC, then mA = _________. mC March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Justification One of the main reasons to study Algebra is to learn how to prove things. The whole business of math is proving things. To prove things in math you must be able to justify everything with legitimate reasons. Our reasons include: postulates, definitions and algebra properties. March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Example Solve 3x + 12 = 8x – 18 and write a reason for each step. 3x + 12 = 8x – 18 Given 3x – 8x + 12 – 12 = 8x – 8x – 18 – 12 Subtraction Property –5x = –30 Simplify (combine like terms) –5x/(–5) = –30/(–5) Division Property x = 6 Simplify March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Another Example (w/o intermediate steps) Solve x+2(x – 3) = 5x + 2 x + 2(x – 3) = 5x + 2 Given x + 2x – 6 = 5x + 2 Distributive Prop. 3x – 6 = 5x + 2 Simplify 3x = 5x + 8 Addition Prop. –2x = 8 Subtraction Prop. x = – 4 Division Prop. March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Before we do a proof… Given Any algebra proof must begin with information that we know is true. This will be given to us as a place to start, so it is called the “given”. There can be one or more givens in a problem. March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties This is “Proof”. If you feel uncomfortable and confused, that’s normal. Everyone is confused with proof at first. There is only one way to learn proof: PRACTICE. You have to know the properties, postulates and definitions. You must diligently practice by doing the homework every night – NO EXCUSES. You learn by making mistakes. Everyone does. March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Proof is essential. Proof is a mandatory part of higher math. If you plan on going to college and/or taking more advanced math you must prove things. Algebra is the place to learn to do this. We will do proofs until the end of the year. Don’t fight it, they are not going to go away. March 27, 2017 Geometry 2.4 Reasoning with Algebra Properties