Review properties of equality and use them to write algebraic proofs.

1. Objectives Review properties of equality and use them to write algebraic proofs.

2. A proof uses logic, definitions, properties, and previously proven statements to “prove” that a conclusion is true. • An important part of writing a proof is giving justifications to show that every step is valid. • Possible ways to “prove” or justify each step: • A definition • A postulate • A property • Something given in the problem

4. Remember! The Distributive Property states that a(b + c) = ab + ac.

5. Example 1: Solving an Equation in Algebra Solve the equation 4m – 8 = –12. Write a justification for each step. 4m – 8 = –12 +8+8 4m = –4 m = –1

6. Solve the equation . Write a justification for each step. t = –14 Check It Out! Example 1

7. Helpful Hint AB AB represents the length AB, so you can think of AB as a variable representing a number. Like algebra, geometry also uses numbers, variables, and operations. For example, segment lengths and angle measures are numbers. So you can use these same properties of equality to write algebraic proofs in geometry.

8. Example 2: Solving an Equation in Geometry Write a justification for each step. NO = NM + MO 4x – 4 = 2x + (3x – 9) 4x – 4 = 5x – 9 –4 = x – 9 5 = x

9. Check It Out! Example 2 Write a justification for each step. mABC = mABD + mDBC 8x°=(3x + 5)°+ (6x – 16)° 8x = 9x – 11 –x = –11 x = 11

10. Check It Out! Example 2 Write a justification for each step. mABC = mABD + mDBC 8x°=(3x + 5)°+ (6x – 16)° 8x = 9x – 11 –x = –11 x = 11

11. Classwork: Exit Ticket with Partner Homework: • 2.5 Practice B Homework Handout • Must write out justification for each step to get credit!!

12. Given z – 5 = –12 Mult. Prop. of = z = –7 Add. Prop. of = Lesson Quiz: Part I Solve each equation. Write a justification for each step. 1.

13. Given z – 5 = –12 Mult. Prop. of = z = –7 Add. Prop. of = Lesson Quiz: Part I Solve each equation. Write a justification for each step. 1.

14. Given 6r – 3 = –2(r + 1) 6r – 3 = –2r – 2 Distrib. Prop. Add. Prop. of = 8r – 3 = –2 8r = 1 Add. Prop. of = Div. Prop. of = Lesson Quiz: Part II Solve each equation. Write a justification for each step. 2.6r – 3 = –2(r + 1)

15. WARM UP Give an example of the following properties: 1. Reflexive Property of Equality: 2. Symmetric Property of Equality: 3. Transitive Property of Equality:

16. Objective: Identify properties of equality and congruence. Remember…..segments with equal lengths are congruent and that angles with equal measures are congruent. So the Reflexive, Symmetric, and Transitive Properties of Equality have corresponding properties of congruence.

18. Remember! Numbers are equal (=) and figures are congruent ().

19. Example 1: Identifying Property of Equality and Congruence Identify the property that justifies each statement. A. QRS  QRS B. m1 = m2 so m2 = m1 C. AB  CD and CD  EF, so AB EF. D. 32° = 32° Reflex. Prop. of . Symm. Prop. of = Trans. Prop of  Reflex. Prop. of =

20. Check It Out! Example 2 Identify the property that justifies each statement. A. DE = GH, so GH = DE. B. 94° = 94° C. 0 = a, and a = x. So 0 = x. D. A  Y, so Y  A Sym. Prop. of = Reflex. Prop. of = Trans. Prop. of = Sym. Prop. of 

21. Lesson Review Identify the property that justifies each statement. 1. x = y and y = z, so x = z. 2. DEF  DEF 3. ABCD, so CDAB. Trans. Prop. of = Reflex. Prop. of  Sym. Prop. of 

22. Classwork/Homework come up with a unique example of each