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Geometry Honors – Proofs

1. If D is in the interior of ABC , then m ABD + m DBC = m ABC. Geometry Honors – Proofs. 2. If M is between X and Y, then XM + MY = XY. Postulates. Remember…. 1. Ruler Postulate 2. Segment Addition Postulate 3. Protractor Postulate

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Geometry Honors – Proofs

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  1. 1. IfD is in the interior ofABC, then m ABD + m DBC = m ABC. Geometry Honors – Proofs 2.If Mis between Xand Y, then XM + MY = XY.

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

  3. 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.

  4. 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.

  5. @ AE EB Sketching the Given Redraw the diagram if the given information also states that

  6. 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.

  7. 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.

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

  9. Geometric Properties • Reflexive Property of Equality • Real Numbers For any real number a, a = a • Segment Length For any segment AB, AB = AB • Angle Measure For any angle A, • Symmetric Property of Equality • Real Number For any real numbers a and b, if a = b, then b = a • Segment Length For any segments AB and CD, if AB = CD, then CD = AB • Angle Measure For any angles A and B, if • Transitive Property of Equality • Real Number For any real numbers a, b and c, if a = b and b = c, then a = c • Segment Length For any segments AB, CD and EF, if AB = CD and CD = EF, then AB = EF • Angle Measure For any angles A, B, and C, if

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

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

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

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

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

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

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