2.5 Reasoning in Algebra and Geometry Algebraic properties of equality are used in Geometry. –Will help you solve problems and justify each step. In Geometry,

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2.5 Reasoning in Algebra and Geometry

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Presentation transcript:

2.5 Reasoning in Algebra and Geometry Algebraic properties of equality are used in Geometry. –Will help you solve problems and justify each step. In Geometry, you accept postulates and properties as true. –Some of the properties you accept as true are the properties of equality from Algebra.

Properties of Equality Let a, b, and c be any real numbers. 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/c = b/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.

Distributive Property Use multiplication to distribute a to each term of the sum or difference within the parentheses. Sum:a (b + c) = ab + ac Difference: a (b – c) = ab – ac

Justifying Steps when Solving an Equation What is the value of x? Justify each step.

Justifying Steps when Solving an Equation angles that form a linear pair are suppl. def. of supplementary angles Substitution Property Simplify Subtraction Property of Equality Division Property of Equality

Properties of Congruence

Using Properties of Equality and Congruence What is the name of the property of equality or congruence that justifies going from the first statement to the second statement? A. 2x + 9 = 19 2x = 10 B. C. Subtraction Property of Equality Transitive Prop. Of Congruence Symmetric Property of Equality

Proof A proof – a convincing argument that uses deductive reasoning. –Logically shows why a conjecture is true. –A two-column proof lists each statement on the left and the reasons on the right. –Each statement must follow logically from the steps before it.

Proof

Writing a Two-Column Proof Write a two-column proof. Given: Prove:

Writing a Two-Column Proof

2.6 – Proving Angles Congruent Vertical Angle Theorem

Homework from textbook. Page ALL