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2.5.1 Reason Using Properties from Algebra
Algebraic Properties of EQUALITY
Let a, b, and c be real numbers
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
ac=bc
Division Property
If a = b and c ≠ 0
a b

c c
Substitution Property
If a = b, then a and b can be substituted in
any equation or expression
Distributive Property
If a = b, then
a(b + c) = ab + ac
You see now why!
 We did the conditional so extensively, we will almost
exclusively live in the T, T, T row
 We will start out doing things that seem like “common sense”
but trust me it will get more difficult!
 You must practice by doing these proofs that are “easy” so
that we can eliminate “simple” mistakes (usually format)
 As we develop our ideas in geometry about the shapes, lines
(chapter 3), triangles (chapter 4, 5), etc. we will need these
tools of logic to understand
 Example 1 on page 105
R, S, T Properties of Equality
Reflexive Property of Equality (useful??)
Real Numbers
For any real number a,
Segment Lengths
For any segment AB,
Angle Measure
For any angle A,
a=a
AB = AB
m A = mA
Symmetric Property of Equality
Real Numbers
For any real numbers a and b,
if
a=b
then
b=a
Segment Lengths
For any segments AB and BC,
if
AB = BA
then
BA = AB
Angle Measure
For any angles A and B,
if
m A = mB
then
mB = m A
Transitive Property of Equality
Real Numbers
For any real numbers a, b, and c,
if
a = b and b = a
then a = c
Segment Lengths
For any segments AB, CD and EF,
if
AB = CD and CD = EF
Angle Measure
For any angles A, B and C,
if m A = mB and mB = m C
then
m A = m C
then
AB = EF
Solve the equation and justify each step
44 - 2(3x + 4) = -18x
44 - 6x - 8 = -18x
- 6x + 36 = -18x
36 = -12x
-3 = x
x = 3
Given
Distributive Property of Equality
CLT
Addition Property of Equality
Division Property of Equality
Symmetric property of Equality
This is an example of a 2 column proof, the left column is the statements, the right
column is the reasons
Homework
 pp. 108

 1 – 29 odd, 30, 31, 39