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

2. 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 and c≠0, then a/c = b/c
Reflexive Property a = a
Symmetric Property If a=b, then b=a
Transitive Property If a=b and b=c, then a=c
Substitution Property If a=b, then b can replace a in any expression

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

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

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

6. Example 3: • M K L N Fill in each missing reason. LM bisects KLN Given
m MLN = m KLM Definition of angle bisector
4x = 2x _____________________
2x = 40 _____________________
x = _____________________
Substitution Prop.
Subtraction Prop. of Equality
Division Prop. Of Equality

7. Example 4: Solve for y and justify each step. 2y 3y-9 A B C
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 Property AB AB
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. 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. Homework
Page 91-93
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