1. Chapter 2: Reasoning and Proof
2.5.1 Reason Using Properties from Algebra

2. 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 a c = b c
Division Property If a = b and c ≠ 0
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

3. 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

4. R, S, T Properties of Equality
Reflexive Property of Equality (useful??)
Real Numbers For any real number a, a = a
Segment Lengths For any segment AB, AB = AB
Angle Measure For any angle A, 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 then AB = 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

5. Solve the equation and justify each step
(3x + 4) = -18x Given
x = -18x Distributive Property of Equality
6x = -18x CLT
36 = -12x Addition Property of Equality
-3 = x Division Property of Equality
x = 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

6. Homework
pp. 108
1 – 29 odd, 30, 31, 39