by: mitch midea, hannah tulloch, rosemary zaleski

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Chapter 3 Geometry Powerpoint. By: Mitch Midea, Hannah Tulloch, Rosemary Zaleski. 3-1. Parallel Lines - ═, are coplanar, never intersect Perpendicular Lines - ┴, Intersect at 90 degree angles Skew Lines - Not coplanar, not parallel, don’t intersect - PowerPoint PPT Presentation

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  • By: Mitch Midea, Hannah Tulloch, Rosemary Zaleski

  • 3-1Parallel Lines- , are coplanar, never intersectPerpendicular Lines- , Intersect at 90 degree anglesSkew Lines- Not coplanar, not parallel, dont intersectParallel Planes- Planes that dont intersect

  • 3-1 (cont.)Transversal- , a line that intersects 2 coplanar lines at 2 different pointsCorresponding
  • 3-1 ExampleCorresponding Angle Theorem

  • 3-2Corresponding
  • 3-2 ExamplesAlternate Interior Angles TheoremAlternate Exterior Angles Theorem

  • 3-3ConversesCorresponding
  • 3-3 ExampleJGH and KHG use the Same Side Interior Theorem

  • 3-4Perpendicular Lines

    Perpendicular Bisector of a Segment- a line perpendicular to a segment at the segments midpointUse pictures from book to show how to construct a perpendicular bisector of a segment The shortest segment from a point to a line is perpendicular to the lineThis fact is used to define the distance from a point to a line as the length of the perpendicular segment from the point to the line

  • 3-4 ExamplecdabCD is a perpendicular bisector to AB, creating four congruent right angles

  • 3-5Slopes of Lines

    Slope- a number that describes the steepness of a line in a coordinate plane; any two points on a line can be used to determine slope (the ratio of rise over run)Rise- the difference in the Y- values of two points on a lineRun- the difference in the X- values of two points on a line

  • 3-5 ExampleSlope is rise over run and expressed in equations as m

  • 3-6Lines in the Coordinate Plane

    The equation of a line can be written in many different forms; point-slope and slope-intercept of a line are equivalentThe slope of a vertical line is undefined; the slope of a horizontal line is zeroPoint-slope: y-y1 = m(x-x1) ; where m is the slope, and (x1,y1) is a given point on the lineSlope-intercept: y=mx+b : where m is the slope and b is the interceptLines that coincide are the same line, but the equations may be written differently

  • 3-6 ExampleSlope-Intercept FormPoint Slope Form