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Transcript 
Chapter 2 Lesson 4
Objective: To connect reasoning
in algebra to geometry.
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
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
A
•B
•
O
•C
AOC.
Example 1:
•
A•
Solve for x and justify each step.
Given: m
AOC = 139
B
x°
O
•C
(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 =
Example 2:
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
Example 3:
Fill in each missing reason.
•
K•
M
L
4x°
LM bisects  KLN
Given
m MLN = m KLM
Definition of angle bisector
4x = 2x + 40
Substitution
Prop.
_____________________
2x = 40
Subtraction
Prop. of Equality
_____________________
x = 20
Division
Prop. Of Equality
_____________________
•N
Example 4:
Solve for y and justify each step.
Given: AC = 21
2y
A
3y-9
B
AB + BC = AC
Segment Addition Postulate
2y + (3y – 9) = 21
Substitution Property
5y – 9 = 21
Simplify
5y = 30
Addition Property of Equality
Y=6
Division Property of Equality
C
Properties of Congruence
Reflexive Property
Symmetric Property
Transitive Property
AB
A  A
If AB  CD, then CD AB
If A B, then  B A
AB
If AB
 CD and CD  EF, then AB  EF
If A  B and B C, then A  C.
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
Transitive Property of Congruence
 PQ.
Homework
Page 91-93
#1-30
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