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Lesson 2-4 Reasoning in Algebra

Lesson 2-4 Reasoning in Algebra. Check Skills You’ll Need. Name 1 in two other ways. Name the vertex of 2. If 1 2 , name the bisector of AOC. If m AOC = 90 and m 1 =45 , find m 2 If m AOC = 90 , name two perpendicular rays. A. 1. O. 2. B. C.

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Lesson 2-4 Reasoning in Algebra

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  1. Lesson 2-4Reasoning in Algebra

  2. Check Skills You’ll Need • Name 1 in two other ways. • Name the vertex of 2. • If 1 2 , name the bisector of AOC. • If m AOC = 90 and m 1 =45, find m 2 • If m AOC = 90, name two perpendicular rays. A 1 O 2 B C

  3. Properties of Equality Addition Property If a = b, then a + c = b + c. Subtraction Property If a = b, then a – c = b – c. Multiplication Property If a = b, then a  c = b  c. Division Property If a = b, then a/c = b/c. Reflexive Property a = a Symmetric Property If a = b, then b = a Substitution Property If a = b, then you may replace b with a inany expression. Transitive Property If a = b and b = c, then a = c. Distributive Propertya(b + c) = ab + ac

  4. Segment Addition Postulate A B C If three points A, B, and C are collinear and B is between A and C, then A + B = AC Angle Addition Postulate If point B is in the interior of AOC, then m AOB + m BOC = m AOC. B A O C

  5. Example: Justifying Steps in Solving an Equation Solve for x and justify each step Given: m AOC = 139 m AOB + m BOC = m AOC x + 2x + 10 = 139 3x +10 = 139 3x = 129 x = 43 B x0 A (2x + 10) 0 O C Angle Addition Postulate Substitution Property Simplify Subtraction Property Division Property

  6. Example: Justifying Steps in Solving an Equation Fill in the missing reason. Given: LM bisects KLN LM bisects KLN m MLN = m KLM 4x = 2x + 40 2x = 40 x = 20 M (2x + 40)0 4x 0 K L N Given Definition of a bisector Substitution Subtraction Property Division Property

  7. Justifying Steps in Solving an Equation Solve for y and justify each step. Given: AC = 21 AB + BC = AC 2y + (3y – 9) = 21 5y – 9 = 21 5y = 30 y = 6 2y 3y - 9 A B C segment addition postulate substitution simplify addition property division property

  8. Properties of Congruence Reflexive Property AB BA A A Symmetric Property If AB CD, then CD AB. If A B, then B A. Transitive Property If AB CD, and CD EF, then AB EF. If A B and B C, then A C.

  9. Using Properties of Equality and Congruence K K If 2x – 8 = 10, then 2x = 18 If RS TW and TW PQ, then RS PQ If m A = m B, then m B = m A XY YX If m A = 45 and 45 = m B, then m A = m B Reflexive Addition Property Transitive Symmetric Symmetric Substitution

  10. It’s TEST TIME folks

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