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Reasoning in Algebra and Geometry Vocabulary ο΅ Proof ο΅ ο΅ A convincing argument that uses deductive reasoning Two-Column Proof ο΅ Lists each statement on the left and the reason (or justification) is on the right Properties of Equality Addition Property πΌπ π = π, π‘βππ π + π = π + π Subtraction Property πΌπ π = π, π‘βππ π β π = π β π Multiplication Property Division Property Reflexive Property Symmetric Property Transitive Property Substitution Property πΌπ π = π, π‘βππ π β π = π β π π π πΌπ π = π πππ π β 0, π‘βππ = π π π=π πΌπ π = π, π‘βππ π = π πΌπ π = π, πππ π = π, π‘βππ π = π πΌπ π = π, π‘βππ π πππ πππππππ π ππ πππ¦ ππ₯ππππ π πππ The Distributive Property ο΅ π π + π = ππ + ππ ο΅ π π β π = ππ β ππ ο΅ 2 π₯+3 = ο΅ 3 π₯β4 = Justifying Steps When Solving an Equation ο΅ What is the value of x? Justify each step. ο΅ β π΄ππ πππ β πππΆ πππ π π’ππππππππ‘πππ¦ (2π₯ + 30) π₯ Justifying Steps When Solving an Equation ο΅ Solve 55π₯ β 3 9π₯ + 12 = β64 and write a reason for each step. Properties of Congruence Using Properties of Equality and Congruence ο΅ What is the name of the property of equality or congruence that justifies going from the first statement to the second? ο΅ 2π₯ + 9 = 19 ο΅ 2x=10 ο΅ β π β β π πππ β π β β πΏ ο΅ β π β β πΏ ο΅ 3(x+5)=9 ο΅ 3x+15=9 Fill in the reason that justifies each step Statement Reasons 1 π₯ β 5 = 10 2 2 1 π₯ β 5 = 10 2 π₯ β 10 = 20 π₯ β 30 Fill in the reason that justifies each step Fill in the reason that justifies each step Name the property! Independent Practice-iWork ο΅ Reasoning in Algebra and Geometry iWork
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