Geometry 2.4 Algebra Properties Essential Question: How do you use algebraic properties to solve equations?

Geometry 2.4 Reasoning with Algebra Properties Topics/Objectives Use properties from algebra. Use properties to justify statements about segment and angle measure. September 21, 2018 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Don’t copy all of this down These properties are all listed on page 92 – use the book. You need to have them all memorized. You had most of of these in Pre algebra and Algebra 1. September 21, 2018 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 September 21, 2018 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 September 21, 2018 Geometry 2.4 Reasoning with Algebra Properties

Multiplication Property If a = b, then ac = bc Example September 21, 2018 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Division Property Division Property Example September 21, 2018 Geometry 2.4 Reasoning with Algebra Properties

Substitution Property If a = b, then a can be substituted for b (or b for a) in any equation or expression. If a = b and a = c, then b = c September 21, 2018 Geometry 2.4 Reasoning with Algebra Properties

Distributive property a(b + c) = ab + ac September 21, 2018 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 A lot like the Law of Syllogism September 21, 2018 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 September 21, 2018 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 September 21, 2018 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 September 21, 2018 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 September 21, 2018 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 September 21, 2018 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Using a Property Symmetric: If AB = CD, then CD = ________ AB September 21, 2018 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 September 21, 2018 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Justification One of the main reasons to study Geometry 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. September 21, 2018 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 –5x/(–5) = –30/(–5) Division Property x = 6 Simplify September 21, 2018 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. September 21, 2018 Geometry 2.4 Reasoning with Algebra Properties

Properties in Geometry Segment Length Angle Measure Reflexive AB = AB mA = mA If mA = mB, then mB = mA Symmetric If AB = CD, then CD = AB If mA = mB, and mB = mC, then mA = mC If AB = CD, and CD = EF, then AB = EF Transitive These properties are all listed on page 94. Use it! September 21, 2018 Geometry 2.4 Reasoning with Algebra Properties

Geometry 2.4 Reasoning with Algebra Properties Before we do a proof… Given Any geometry 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. September 21, 2018 Geometry 2.4 Reasoning with Algebra Properties

Using Geometry Properties AC = BD. Prove that AB = CD. A B C D AC = BD Given AB + BC = AC BC + CD = BD Seg. Add. Post Seg. Add. Post AB + BC = BC + CD Substitution AB = CD Subtraction September 21, 2018 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. September 21, 2018 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. Geometry 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. September 21, 2018 Geometry 2.4 Reasoning with Algebra Properties