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2.5 Reasoning with properties from Algebra

2.5 Reasoning with properties from Algebra . GEOMETRY. Goal 1: Using Properties from Algebra – Properties of Equality. In all of the following properties – Let a, b, and c be real numbers. Properties of Equality. Addition property: If a = b, then a + c = b + c Subtraction property:

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2.5 Reasoning with properties from Algebra

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  1. 2.5 Reasoning with properties from Algebra GEOMETRY

  2. Goal 1: Using Properties from Algebra – Properties of Equality In all of the following properties – Let a, b, and c be real numbers

  3. Properties of Equality • 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 ca = cb • Division property: If a = b, then for c  0

  4. Addition Property This is the property that allows you to add the same number to both sides of an equation.

  5. Subtraction Property This is the property that allows you to subtract the same number to both sides of an equation.

  6. Multiplication Property This is the property that allows you to multiply the same number to both sides of an equation.

  7. Division Property This is the property that allows you to divide the same number to both sides of an equation.

  8. More Properties of Equality • Reflexive Property: a = a. • Symmetric Property: If a = b, then b = a. • Transitive Property: If a = b, and b = c, then a = c.

  9. Reflexive Property: a = a I know what you are thinking, duh this doesn’t seem too difficult to grasp. Just remember this one, when we begin to prove that triangles are congruent.

  10. Symmetric Property: a = b so b = a I know another duh property. Just remember when you get an answer that is a little different than the one you are use to getting. (Do we like To always have x or y on the left side of the equal sign?) For example: 2 – y = 10

  11. Transitive Property This one is many times confused with substitution property of equality. Remember transitive is like “transit” which means to move. Think of there being 3 bus stops: a, b, and c. If you move from a to b, then from b to c, it would have been the same as moving from a to c directly.

  12. Substitution Property of Equality If a = b, then a may be substituted for b in any equation or expression. You have used this many times in algebra.

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

  14. Properties of Congruence • Reflexive object A  object A • Symmetric If object A  object B, then object B  object A • Transitive If object A  object B and object B  object C, then object A  object C

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