Section 2.4 Algebraic Reasoning

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Presentation transcript:

Section 2.4 Algebraic Reasoning Student Learning Goal: Students will justify steps for solving equations using Algebraic Properties of Equality and then apply those properties to segment lengths and angle measurements Homework: Worksheet

Solving an equation, you used properties of real numbers Examples: 1) 4x + 5 = 21 2) 3( 2x +5) = 21 Segment lengths and angle measurements are real numbers, so you can use these properties to write logical arguments about geometric figures.

Example 1: State the property that justifies each statement. If m ∠A = m∠B and m∠B = m∠C, then m∠A =m∠C If m ∠1 + m∠2 = 90 and m∠2 = m∠3, then m∠1 + m∠3 = 90 ∠A = ∠A If JK ≅ LM, then LM ≅ JK If HJ + 5 = 20 , then HJ = 15 If AB = 14 and CD = 1, then AB = CD

Example 2: Solve 3x + 2 = 23-4x Justify each step. Equation Reason 3x + 2 = 23 - 4x Given 3x + 2-2 = 23 - 2 - 4x __________________ 3x = 21 - 4x Substitution/Simplify 3x + 4x = 21 - 4x + 4x ____________________ 7x = 21 7 7 Division Property x = 3

Example 3: Solve : 5(7x - 8) = 30 Justify each step Example 3: Solve : 5(7x - 8) = 30 Justify each step. Show 2 different ways. 1st way: 2nd way: Equation Reason 5( 7x - 8) =30 Given 35x -40 = 30 __________________ 35x -40 + 40 = 30 + 40 35x = 70 ______________________________________ 35 35 x = 2