Reasoning with Properties from Algebra Chapter 2.6 Run Warmup.

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Reasoning with Properties from Algebra Chapter 2.6 Run Warmup

Properties of Equality Addition (Subtraction) Property of Equality If a = b, then: a + c = b + c a – c = b – c If x + 8 = 20, Then x = 12 Why? Subtract Prop. of =

Properties of Equality Multiplication (Division) Property of Equality If a = b, then: ac = bc If 4x = 32, Then x = 8 Why? Division Prop. of =

Properties of Equality Reflexive Prop. of = a = a m  A = m  A Why? Reflex Prop = Symmetric Prop. of = If a = b, then b = a. If 54 o = m  C, then m  C = 54 o Why? Symm. Prop =

Properties of Equality Transitive Prop. of = If a = b and b = c, then a = c If 2x = y and y = 48, then 2x = 48 Why? Transitive Prop. Substitution Prop. of = If a = b, then a can replace b in an equation If 4x + 5 = 3y and x =-2, then 4(-2) + 5 = 3y Why? Substitution Prop.

Distributive Property a(b + c) = ab + ac. a(b – c) = ab – ac. -x(3x + 2) = 27 -3x 2 – 2x = 27 Why? Distributive Prop.

Solve: 5x – 18 = 3x + 2 and give a reason for each step. 5x – 18 = 3x + 2Given StepReason 2x – 18 = 2Subtraction Prop = 2x = 20Addition Prop = x = 10Division Prop =

Solve: 55z – 3(9z + 12) = -64 and give a reason for each step. 55z – 3(9z + 12) = -64Given StepReason 55z – 27z – 36 = -64Distributive Prop 28z – 36 = -64Combining like terms 28z = -28Addition Prop = z = -1Division Prop = Not Multiplication Property!!!

What is the reason for each step in the solution? – 8n = –62. Multiplication Property 1. Given1. StepReason 3. – 8n = –163. Subtraction Property 4. n = 24. Division Property

3. 10 – 8n = –63. Substitution – 10 – 8n = – 6 – 104. Subtraction Property 5. –8n = –165. Substitution 7. n = 27. Substitution StatementsReasons Proof: 1. Given Division Property 2.2. Multiplication Property This is how the Textbook will show that same problem.

Geometric Properties of Equality For any segment AB, AB = AB For any angle A, m  A = m  A Segment Length Angle Measure If AB = CD, then CD = AB If m  A = m  B, then m  B = m  A If AB = CD and CD = EF, then AB = EF. If m  A = m  B and m  B = m  C, then m  A = m  C. Reflexive Prop. = Symmetric Prop. = Transitive Prop. =

Given: AB = CD. Prove: AC = BD. AB = CDGiven StepReason AB + BC = BC + CDAddition Prop. = AC = AB + BCSegment Addition Postulate BD = BC + CDSegment Addition Postulate AC = BDSubstitution Prop = ABCD

1.A 2.B 3.C 4.D A.I only B.I and II C.I and III D.II and III

Chapter 2-6 Pgs – 6 all 9 – 19 odd 33, 39 Homework