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Understanding Properties of Equality in Algebra and Geometric Proofs

This lesson explores the use of logical reasoning and properties of equality in algebraic and geometric proofs. Students will learn key properties such as the Addition, Subtraction, Multiplication, and Division Properties of Equality. Additionally, the lesson covers the Reflexive, Symmetric, Transitive, and Distributive Properties, along with important theorems like the Midpoint Theorem and Angle Bisector Theorem. Through various exercises, students will develop skills to justify statements and apply properties effectively in problem-solving scenarios.

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Understanding Properties of Equality in Algebra and Geometric Proofs

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Presentation Transcript

  1. Section 2-4: Reasoning in Algebra Goal 2.01: Use logic and deductive reasoning to draw conclusions and solve problems.

  2. Turn in Homework • Lesson Quiz 2-3

  3. Essential Question How are properties of equality used in Algebraic and Geometric Proofs?

  4. Addition Property of Equality If a = b and c = d, then a + c = b + d.

  5. subtraction property of equality If a = b and c = d, then a – c = b – d.

  6. multiplication property of equality If a = b then ac = bc.

  7. division property of equality If a = b and c ≠ 0, then a = b . c c

  8. substitution property If a = b then either a or b may be substituted for the other in any equation or inequality.

  9. reflexive (identity) Property a = a DE = DE  1 =  1

  10. Symmetric Property If a = b then b = a.

  11. Distributive Property a ( b + c ) = ab + ac a ( b – c) = ab - ac

  12. Transitive Property If a = b and b = c, then a = c. If DE = FG and FG = JK, then DE = JK. If 1 = 2 and 2=3, then 1 = 3.

  13. Midpoint Theorem If M is the midpoint of AB, then AM = ½ AB and MB = ½ AB, also 2 AM = AB and 2MB = AB.

  14. Angle Bisector Theorem If BX is the bisector of  ABC, then 2 m ABX = m ABC and m ABX = m ABC. 2 m XBC = m ABC and m XBC = m ABC.

  15. Review: Definition of midpoint Definition of angle bisector Angle Addiction Postulate Segment Addition Postulate

  16. Compare the definition of midpoint to the Midpoint Theorem?

  17. Compare the definition of the angle bisector and the Angle Bisector Theorem?

  18. Examples • Worksheet Labeled: Justify the Statements examples • Together: p 92 (5 – 24 all)

  19. Group Work Practice 2-4 2 – 14 evens

  20. Individual Work Practice 2-4: 1 – 13 odds

  21. Assess Lesson Quiz 2 – 4: for a grade

  22. Homework Worksheet back on Front: Labeled: Properties of Algebra Justify the Statement Homework

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