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Geometry Honors – Proofs 1. If D is in the interior of ABC, then m ABD + m DBC = m ABC. 2. If M is between X and Y, then XM + MY = XY.

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Postulates Remember…. 1. Ruler Postulate 2. Segment Addition Postulate 3. Protractor Postulate 4. Angle Addition Postulate

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Postulates Postulate 5 – Through any two points there exists exactly one line. Postulate 6 – A line contains at least two points. Postulate 7 – If two lines intersect, then their intersection is exactly one point. Postulate 8 – Through any three noncollinear points there exists exactly one plane. Postulate 9 – A plane contains at least three noncollinear points.

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Postulates Postulate 10 – If two points lie in a plane, then the line containing them lies in the plane. Postulate 11 – If two planes intersect, then their intersection is a line.

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Sketching the Given AEEB Redraw the diagram if the given information also states that

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Interpret Which of the following statements cannot be assumed from the diagram? All points are coplanar. CEF FED CEF and FED are a linear pair.

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Reason Using Properties from Algebra Remember….. 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 ac = bc Division Property? – If a = b and c ≠ 0 then a/c = b/c Substitution Property? – If a = b, then a can be substituted or b in any equation or expression.

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Write reasons for each step Solve 3x + 8 = -4x - 34. Write a reason for each step. Equation ExplanationReason 3x + 8 = -4x - 34 Write original equation. Given 3x + 8 + 4x = -4x – 34 + 4x Add 4x to each side. Addition Property of Equality 7x + 8 = -34 Combine like terms. Simplify. 7x – 8 = -34 - 8 Subtract 8 from each side. Subtraction Property of Equality x = -6 Divide each side by 7. Division Property of Equality 7x = -42 Combine like terms. Simplify. Combine like terms. Simplify.

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Geometric Properties

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In the diagram, WY = XZ. Show that WX = YZ. EquationExplanationReason

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In the diagram, WY = XZ. Show that WX = YZ. EquationExplanationReason WY = XZUse given informationGiven

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In the diagram, WY = XZ. Show that WX = YZ. EquationExplanationReason WY = XZUse given informationGiven WY = WX + XYAdd lengths of adjacent segments Segment Addition Postulate

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In the diagram, WY = XZ. Show that WX = YZ. EquationExplanationReason WY = XZUse given informationGiven WY = WX + XYAdd lengths of adjacent segments Segment Addition Postulate XZ = XY + YZAdd lengths of adjacent segments Segment Addition Postulate

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In the diagram, WY = XZ. Show that WX = YZ. EquationExplanationReason WY = XZUse given informationGiven WY = WX + XYAdd lengths of adjacent segments Segment Addition Postulate XZ = XY + YZAdd lengths of adjacent segments Segment Addition Postulate WX + XY = XY + YZSubstitute WX + XY for WY and XY + YZ for YZ. Substitution Property of Equality

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In the diagram, WY = XZ. Show that WX = YZ. EquationExplanationReason WY = XZUse given informationGiven WY = WX + XYAdd lengths of adjacent segments Segment Addition Postulate XZ = XY + YZAdd lengths of adjacent segments Segment Addition Postulate WX + XY = XY + YZSubstitute WX + XY for WY and XY + YZ for YZ. Substitution Property of Equality WX = YZSubtract XY from each side.Subtraction Property of Equality

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