1. 2.4 Reasoning with Properties from Algebra
CAS 3
Goal 1: Use properties from algebra
Goal 2: Use properties of length and measure to justify segment and angle relationships

2. Algebraic Properties of Equality
Addition Property
If a=b, then a+c=b+c
Subtraction Property

3. Algebraic Properties of Equality continued-
Multiplication Property
If a=b, then ac=bc
Division Property
If a=b, then ,

4. Algebraic Properties of Equality continued-
Reflexive Property
For any real number a, a=a.
Symmetric Property
If a=b, then b=a

5. Ex. 1 Solve the Equation below and write a reason for each step.

6. Ex. 2 Below is the formula to convert Fahrenheit to Celsius
Ex. 2 Below is the formula to convert Fahrenheit to Celsius. Solve the formula for F and write the reason for each step.

7. Algebraic Properties of Equality continued-
Transitive Property
If a=b and b=c, then a=c.
Substitution Property
If a=b, then “a” can be substituted for “b” in any equation or expression.

8. Distributive Property
a(b+c)=ab+ac Or

9. Properties of Equality
Reflexive Property, Symmetric Property, Transitive Property can be used with segment lengths and angle measurements.

10. Ex. 3 AC=BD. Verify that AB=CD
Statements ___Reasons 1. AC=B D 2. BC=BC 3. AC-BC=BC-BC 4. AB+BC=AC, BC+CD=BD 5. AB=AC-BC, CD=BD-BC 6. AB=CD