Reasoning with 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.

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Presentation transcript:

Reasoning with 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: Reflexive Property: For any real number a,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 a can be substituted for b in any equation or expression. Distributive Property: a(b+c)=ab+ac.

Last year in algebra, you learned to solve equations. This year, one of the key concepts that you will learn is how to write a proof. We will be using a format called a two column proof. In the first column, you will show the steps; in the second column, you will give the reason why you know each step is valid. Example: Solve 5x-18=3x+2 in two column form: Solution: The algebraic properties of equality can be used in geometry.

Example: Given the following diagram prove: If AB=CD, then AC=BD. Solution: (Note: When proving a conditional statement, the given is always the hypothesis of the statement and the conclusion will always be the last statement:

Example: In the above diagram: Solution: