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

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

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

7. Like algebra, geometry also uses numbers, variables, and operations
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.
A B
AB represents the length AB, so you can think of AB as a variable representing a number.
Helpful Hint

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

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

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

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

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