2.4 Reasoning with Properties from Algebra

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Presentation transcript:

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

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

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

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

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

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.

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.

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

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

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