1. Lesson 2-4 Reasoning in Algebra

2. Check Skills You’ll Need 1.Name 1 in two other ways. 2.Name the vertex of 2. 3.If 1 2, name the bisector of AOC. 4.If m AOC = 90 and m 1 =45, find m 2 5.If m AOC = 90, name two perpendicular rays. A O 1 2B 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 Propertya = a Symmetric PropertyIf 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 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. ABC A O B 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 x0x0 (2x + 10) 0 A O B 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 (2x + 40) 0 4x 0 K L M 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 ABC 2y3y - 9 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 Substitution

10. It’s TEST TIME folks