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2.4 Reasoning in Algebra

2.4 Reasoning in Algebra. Chapter 2. Properties of Equality (pg 89 in text). 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 a · c = b · c

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2.4 Reasoning in Algebra

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  1. 2.4 Reasoning in Algebra Chapter 2

  2. Properties of Equality (pg 89 in text) • 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 a·c = b ·c • Division Property If a = b and c = 0, then a = b c c • Reflexive Property 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 b can replace a in any expression

  3. The Distributive Property *You also assume that other properties from Algebra are true. • Distributive Property a(b + c) = ab + ac

  4. Justifying Steps in an Equation Solve for x and justify each step. B Given: m< AOC = 139 A x (2x + 10) O C m< AOB + m< BOC = m< AOC Angle Addition Postulate x + 2x + 10 = 139 Substitution Property Simplify 3x + 10 = 139 Subtraction Property 3x = 129 x = 43 Division Property

  5. Fill in each missing Reason: Given: LM bisects <KLN LM bisects <KLN Given m<MLN = m<KLM Definition of Angle Bisector 4x = 2x + 40 2x = 40 x = 20 M K (2x + 40) 4x N L Substitution Property Subtraction Property Division Property

  6. Solve for y and Justify each step. Given: AC = 21 2y 3y - 9 B C A AB + BC = AC Segment Addition Property 2y + 3y – 9 = 21 Substitution Property Simplify 5y – 9 = 21 Addition Property 5y = 30 Division Property y = 6

  7. Properties of Congruence • Reflexive Property AB = AB <A = <A • Symmetric Property If AB = CD, then CD = AB • Transitive Property If AB = CD and CD = EF, then AB = EF If <A = <B and <B = <C, then <A = <C

  8. Using Properties of Equality and Congruence Name the property of equality or congruence that justifies each statement. • <K = <K • If 2x – 8 = 10, then 2x = 18 • If RS = TW and TW = PQ, then RS = PQ. • If m<A = m<B, then m<B = m<A Reflexive Property Addition Property Transitive Property Symmetric Property

  9. Fill in the reason that justifies each step: E Solve for x: m<CDE + m<EDF = 180 x + (3x + 20) = 180 4x + 20 = 180 4x = 160 x = 40 x (3x + 20) C D F a. Angle Addition Postulate b. Substitution Property c. Simplify d. Subtraction Property e. Division Property

  10. Fill in the reason that justifies each step: Solve for n. Given: XY = 42 XZ + ZY = XY 3(n + 4) + 3n = 42 3n + 12 + 3n = 42 6n + 12 = 42 6n = 30 n = 5 3(n + 4) 3n X Z Y a. Segment Addition Postulate b. Substitution Property c. Distributive Property d. Simplify e. Subtraction Property f. Division Property

  11. Homework • Pg 91 1-24, 27-31

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