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Lesson 2-4 Reasoning in Algebra

This lesson focuses on vital reasoning skills needed in algebra, including understanding basic properties of equality and congruence. Key topics covered include the definitions of vertices, angle bisectors, and perpendicular rays, as well as the addition and subtraction properties of equality. Learn how to solve equations and justify each step using postulates, such as the angle addition postulate and segment addition postulate. Practice solving for variables through various examples and solidify your grasp of these foundational concepts in algebra.

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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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