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Ch. 2-5: Reasoning by Using Properties of Algebra

Ch. 2-5: Reasoning by Using Properties of Algebra. Mr. Schaab’s Geometry Class Our Lady of Providence Jr.- Sr . High School 2014-2015. Algebraic Properties. On iTeach , open the documents folder and open the Ch. 2-5 Properties of Algebra Study Guide.

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Ch. 2-5: Reasoning by Using Properties of Algebra

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  1. Ch. 2-5: Reasoning by Using Properties of Algebra Mr. Schaab’s Geometry Class Our Lady of Providence Jr.-Sr. High School 2014-2015

  2. Algebraic Properties • On iTeach, open the documents folder and open the Ch. 2-5 Properties of Algebra Study Guide. • Copy into your notes the algebraic properties listed on the first page. • Make sure you title them appropriately, because you will be referring to these properties and using deductive reasoning to form logical arguments. (these are some of your “known facts”)

  3. Point, Line, and Plane Postulates • Ruler Postulate: The distance between two points A and B on a number line is the absolute value of the difference of the coordinates of A and B. • Segment Addition Postulate: If B is between A and C on a segment, then AB + BC = AC. • Protractor Postulate: The measure of ∠AOB is equal to the absolute value of the difference between the degree measures of Ray OA and Ray OB. • Angle Addition Postulate: If Q is in the interior of ∠RST, then m∠RST = m∠RSQ + m∠QST

  4. Point, Line, and Plane Postulates • Postulate 5 – Through any two points there exists exactly one line. • Postulate 6 – A line contains at least two points. • Postulate 7 – If two lines intersect, their intersection is exactly one point. • Postulate 8 – Through any three noncollinear points there exists exactly one plane. • Postulate 9 – A plane contains at least three noncollinear points. • Postulate 10 – If two points lie in a plane, then the line containing them lies in the plane. • Postulate 11 – If two planes intersect, their intersection is a line.

  5. Logical Arguments • Study the solved equation. Give the proper reason for each step. • 3x – 12 = 7x + 8 -4x – 12 = 8 -4x = 20 x = -5 • 5(x-1) + 3x = 19 5x – 5 + 3x = 19 8x – 5 = 19 8x = 24 x = 3 Given Subtraction Property of Equality Addition Property of Equality Division Property of Equality Given Distributive Property Simplify (Combine Like Terms) Addition Property of Equality Division Property of Equality

  6. Logical Arguments B • Use Deductive Reasoning to prove that the perimeter of triangle ABD is equal to the perimeter of triangle CBD. A C D AB = CB, AD = CD BD = BD AB + AD = CB + AD AB + AD = CB + CD AB + AD + BD = CB + CD + BD Given Reflexive Property Addition Property Substitution Property Addition Property

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