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Geometry 2.5 Big Idea: Reason Using Properties from Algebra

Geometry 2.5 Big Idea: Reason Using Properties from Algebra. Algebraic Properties of Equality. Addition Property If a = b, then a + c = b + c Subtraction Property If a = b, then a - c = b – c (This is what we do when we solve equations.). Multiplication Property If a = b, then ac = bc

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Geometry 2.5 Big Idea: Reason Using Properties from Algebra

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  1. Geometry 2.5 Big Idea: Reason Using Properties from Algebra

  2. Algebraic Properties of Equality Addition Property If a = b, then a + c = b + c Subtraction Property If a = b, then a - c = b – c (This is what we do when we solve equations.)

  3. Multiplication Property If a = b, then ac = bc Division Property If a = b and c ≠ 0, then a = b c c

  4. Substitution Property If a = b, then ‘a’ can be substituted for ‘b’ in any equation. (and vice-versa) Distributive Property a(b + c) = ab + ac

  5. Reflexive Property of Equality Real Numbers: a = a Segment Length: AB = AB Angle Measure: m A = m A

  6. Symmetric Property of Equality Real Numbers: if a = b, then b = a Segment Length: ifAB = CD, then CD = AB Angle Measure: ifm A = m B, then m B = m A,

  7. Transitive Property of Equality Real Numbers: ifa = b and b = c, then a = c Segment Length: if AB = CD and CD = EF, then AB = EF Angle Measure: if m A = m B and m B = m C, then m A=m C

  8. Example: Solve. Write a reason for each step. Given Add. Prop. Of Eq. Sub. Prop. Of Eq. Div. Prop. Of Eq.

  9. Example: Solve. Write a reason for each step.

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