2-5 Reason Using Properties from Algebra Hubarth Geometry.

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Presentation transcript:

2-5 Reason Using Properties from Algebra Hubarth Geometry

Key Concepts Algebraic Properties of Equality Let a, b, and c be real numbers. Addition PropertyIf a = b, then a + c = b + c Subtraction PropertyIf a = b, then a – c = b – c Multiplication PropertyIf a = b, then ac = bc Division PropertyIf a = b, and Substitution PropertyIf a = b, then a can be substituted for b in any equation or expression

Solve 2x + 5 = 20 – 3x. Write a reason for each step. Equation ExplanationReason 2x + 5 = 20 – 3xWrite original equation. Given 2x x =20 – 3x + 3xAdd 3x to each side. Addition Property of Equality 5x + 5 = 20Combine like terms. Simplify. 5x = 15 Subtract 5 from each side. Subtraction Property of Equality x = 3Divide each side by 5. Division Property of Equality Ex 1 Write reasons for Each Step

Key Concepts Distributive Property a(b + c) = ab + ac, where a, b, and c are real numbers. Ex 2 Use the Distributive Property Solve -4(11x + 2) = 80. Write a reason for each step. Equation ExplanationReason –4(11x + 2) = 80 Write original equation. Given –44x – 8 = 80 Multiply. Distributive Property –44x = 88Add 8 to each side. Addition Property of Equality x = –2 Divide each side by –44. Division Property of Equality

Key Concept Reflexive Property of Equality Real NumbersFor any real numbers a, a = a Segment LengthFor any segment AB, AB = AB Angle MeasuresFor any angle A, Symmetric Property of Equality Real NumbersFor any real number a and b, if a = b, then b = a Segment LengthFor any segment AB and CD, if AB = CD, then CD = AB Angle MeasureFor any angles A and B, if Transitive Property of Equality Real NumbersFor any real number a, b, and c, if a = b and b = c, then a =c Segment LengthFor any segments AB, CD and EF, if AB =CD and CD = EF, then AB = EF Angle MeasureFor any angles, A, B, and C, if

Ex 3 Use Properties of Equality Equation ExplanationReason Marked in diagram. Given Add measures of adjacent angles. Angle Addition Postulate Substitution Property of Equality Add measures of adjacent angles Angle Addition Postulate Transitive Property of Equality

In the diagram, AB = CD. Show that AC = BD. Equation ExplanationReason AB = CD Marked in diagram.Given AC = AB + BC Add lengths of adjacent segments. Segment Addition Postulate BD = BC + CD Add lengths of adjacent segments. Segment Addition Postulate Ex 4 Use Properties of Equalities AB + BC = CD + BC Add BC to each side of AB = CD. Addition Property of Equality AC = BD Substitute AC for AB + BC and BD for BC + CD. Substitution Property of Equality