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Section 2.4: Properties of Equality and Algebraic Proofs

Section 2.4: Properties of Equality and Algebraic Proofs. October 5, 2009. Addition. If a=b, then a + c = b + c If x – 5 = 7, then x = 12 Since x – 5 + 5 = 7 + 5 This can be used with Angles and Segments as well If <A = <B , then <A + 90 = <B + 90. Subtraction.

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Section 2.4: Properties of Equality and Algebraic Proofs

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  1. Section 2.4: Properties of Equality and Algebraic Proofs October 5, 2009

  2. Addition • If a=b, then a + c = b + c • If x – 5 = 7, then x = 12 • Since x – 5 + 5 = 7 + 5 • This can be used with Angles and Segments as well • If <A = <B , then <A + 90 = <B + 90

  3. Subtraction • If a=b, then a - c = b - c • If x + 3 = 10, then x = 7 • Since x + 3 - 3 = 10 - 3 • This can be used with Angles and Segments as well • If <A + <B = 180, then <A = 180 - <B • Since <A + <B - <B = 180 - <B

  4. Multiplication • If a=b, then ac = bc • If ½x = 5, then x = 10 • Since 2(½x) = 2(5) • This can be used with Angles and Segments as well • If <A = 45, then 2(<A) = 90 • Since 2(<A) = 2(45)

  5. Division • If a=b, then a / c = b / c (if c is not 0) • If 4x = 12, then x = 3 • Since 4x / 4 = 12 / 4 • This can be used with Angles and Segments as well • If 2AB = 20, then AB = 10 • Since 2AB / 2 = 20 / 2

  6. Distributive • If a ( b + c), then ab + ac • If 2( x + 6) = 10, then 2x + 12 = 10 • This can be used with Angles and Segments as well • If 3(AB + BC) = 21, then 3AB + 3BC = 21

  7. Substitution • If a = b and a = c, then b = c • If x + 5 = y and x = 4, then y = 9 • Since 4 + 5 = y, so 9 = y and y = 9 • This can be used with Angles and Segments as well • If <A + <B = 180 and <B = <C, then <A + <C = 180

  8. Reflexive, Symmetric, Transitive • Reflexive: • a = a • x = x • <A = <A • Symmetric: • If a = b, then b = a • If x + 5 = 15, then 15 = x + 5 • If 90 = <A, then <A = 90 • Transitive: • If a = b and b = c, then a = c • If x + 5 = y, and y = 10, then x + 5 = 10 • If <A + <B = <C and <C = 90, then <A + <B = 90

  9. Practice – Name the Property of Equality • If x + 5 = -11, then x = -16 • If AB+BC=AC and AC=10, then AB+BC=10 • If <C=90 and <B=90, then <C=<B • If 3x + 5= 12, then x + 5/3 = 4 • If -2/3x = 4, then x = -6

  10. Homework – Practice Workbook 2.4 #1-8

  11. Proofs • Formal Proof – a two column proof of statements and reason which follows a step-by-step procedure to reach a conclusion. THESE ARE THE KIND WE WILL USE. • There are also: • Informal Proofs, which are a paragraph describing each step. • Flow Proof, which show each step in a flow chart.

  12. Formal Proofs LOOK AT THE PROOFS ON PW 2-4. You will always be given 2 things in a Formal Proof. • Given: This is your 1st statement • Prove: This is your last statement Statement #2 is always based on what you are given. Statements #3-5 are based on what additional things you need for your prove statement.

  13. ALGEBRAIC PROOFS HANDOUT FOR PRACTICE

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