1. Chapter 2 Lesson 4 Objective: To connect reasoning in algebra to geometry.

2. Properties of Equality Addition PropertyIf a=b, then a+c = b+c Subtraction PropertyIf a=b, then a-c = b-c Multiplication PropertyIf a=b, then ac = bc Division PropertyIf a=b and c≠0, then a/c = b/c Reflexive Propertya = a Symmetric PropertyIf a=b, then b=a Transitive PropertyIf a=b and b=c, then a=c Substitution PropertyIf a=b, then b can replace a in any expression

3. B O C Angle Addition Postulate The Distributive Property a(b+c) = ab + ac If point B is in the interior of AOC, then m AOB + m BOC = m AOC. A

4. Solve for x and justify each step. Given: Given: m AOC = 139 Example 1: A B C O x° (2x + 10)° m AOB + m BOC = m AOC Angle Addition Postulate x + 2x + 10 = 139 Substitution Property 3x + 10 = 139 Simplify 3x = 129 Subtraction Property of = x = 43 Division Property of =

5. Example 2: 5x – 12 = 32 + x Justify each step used to solve 5x – 12 = 32 + x for x. 5x = 44 + x 4x = 44 X = 11 Addition Property of Equality Subtraction Property of Equality Division Property of Equality

6. K M N L (2x + 40)° 4x° Example 3: Fill in each missing reason. LM bisects KLNGiven m MLN = m KLMDefinition of angle bisector 4x = 2x + 40_____________________ 2x = 40_____________________ x = 20_____________________ Substitution Prop. Subtraction Prop. of Equality Division Prop. Of Equality

7. Example 4: y Solve for y and justify each step. 2y3y-9 ABC Given: AC = 21 AB + BC = AC 2y + (3y – 9) = 21 5y – 9 = 21 5y = 30 Y = 6 Segment Addition Postulate Substitution Property Simplify Addition Property of Equality Division Property of Equality

8. Properties of Congruence Reflexive PropertyAB AB A A Symmetric PropertyIf 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. Example 5: Name the property of equality or congruence that justifies each statement. a. K K Reflexive Property of Congruence b. If 2x – 8 = 10, then 2x = 18 Addition Property of Equality c. If x = y and y + 4 = 3x, then x + 4 = 3x. Substitution Property of Equality d. If RS TW and TW PQ, then RS PQ. Transitive Property of Congruence

10. Assignment Page 91-93 #1-30