Algebra and Geometry Reasoning: Concepts and Proofs
Explore key concepts in algebra and geometry reasoning, including properties of equality, distributive property, and proofs using deductive reasoning. Practice solving equations, identifying properties of congruence, and writing two-column proofs to justify mathematical statements.
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2-5 Reasoning in Algebra and Geometry
Problem 1: Justifying Steps when Solving an Equation What is the value of x? Justify each step + + = = 1) 2)2 3)3 4)3 5) 180 AOM x x x x = MOC = + + = 30 30 180 150 50 180 x
Problem 1: Justifying Steps when Solving an Equation What is the value of x? Justify each step = 1) 2) 3) 2 75 75 x x = x = 75 x
Problem 2: Using Properties of Equality and Congruence What is the name of the property of equality or congruence that justifies going from the 1ststatement to the second statement?
What is the name of the property of equality or congruence that justifies going from the 1ststatement to the second statement?
What is the name of the property of equality or congruence that justifies going from the 1ststatement to the second statement?
Proof: a convincing argument that uses deductive reasoning (shows why a conjecture is true) Two-Column Proof: lists each statement on the left and the justification or reason for each statement on the right. Each step must follow logically from the steps before it.
Problem 3: Writing a Two-Column Proof = = + = + = 1) 2) 3) 4) m 1 3 m m m m + = m 2 1 1 2 m m m + 2 2 3 2 m m AEC DEB 3 2 = m 5) m AEC m DEB
= = + + 1) 2) 3) 4) 5) BC AB AB BC AB AB CD CD BC BC BC CD BC = = = + BC AC CD + = BD 6) AC 7) AC BC
