1 / 14

By: Mitch Midea, Hannah Tulloch, Rosemary Zaleski

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

binah
Download Presentation

By: Mitch Midea, Hannah Tulloch, Rosemary Zaleski

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Chapter 3 Geometry Powerpoint By: Mitch Midea, Hannah Tulloch, Rosemary Zaleski

  2. 3-1 • Parallel Lines- ═, are coplanar, never intersect • Perpendicular Lines- ┴, Intersect at 90 degree angles • Skew Lines- Not coplanar, not parallel, don’t intersect • Parallel Planes- Planes that don’t intersect

  3. 3-1 (cont.) • Transversal- ≠, a line that intersects 2 coplanar lines at 2 different points • Corresponding <s- lie on the same side of the transversal between lines • Alt. Int. <s- nonadjacent <s, lie on opposite sides of the transversal between lines • Alt. Ext. <s- Lie on opposite sides of the transversal, outside the lines • Same Side Int. <s- aka Consecutive int. <s, lie on the same side of the transversal between lines

  4. 3-1 Example Corresponding Angle Theorem

  5. 3-2 • Corresponding <s Postulate- if 2 parallel lines are cut by a transversal, the corresponding <s are = • Alt. Int. < Thm.- if 2 parallel lines are cut by a transversal, the pairs of alt. int. <s are = • Alt. Ext. < Thm.- if 2 parallel lines are cut by a transversal, the 2 pairs of alt. ext. <s are = • Same Side Int. < Thm.- if 2 parallel lines are cut by a transversal, the 2 pairs of SSI <s are supp.

  6. 3-2 Examples Alternate Interior Angles Theorem Alternate Exterior Angles Theorem

  7. 3-3 Converses • Corresponding <s Thm.- if 2 coplanar lines are cut by a transversal so that a pair of corresponding <s are =, the 2 lines are parallel • Alt. Int. < Thm.- if 2 coplanar lines are cut by a transversal so that a pair of alt. int. <s are =, the lines are parallel • Alt. Ext. < Thm.- if 2 coplanar lines are cut by a transversal so that a pair of alt. ext. <s are =, the lines are parallel • SSI < Thm.- if 2 coplanar lines are cut by a transversal so that a pair of SSI < are =, the lines are parallel

  8. 3-3 Example ∠JGH and ∠KHG use the Same Side Interior Theorem

  9. 3-4 Perpendicular Lines • Perpendicular Bisector of a Segment- a line perpendicular to a segment at the segments midpoint • Use 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 line • This 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

  10. 3-4 Example c a b d CD is a perpendicular bisector to AB, creating four congruent right angles

  11. 3-5 Slopes 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 line • Run- the difference in the X- values of two points on a line

  12. 3-5 Example Slope is rise over run and expressed in equations as m

  13. 3-6 Lines 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 equivalent • The slope of a vertical line is undefined; the slope of a horizontal line is zero • Point-slope: y-y1 = m(x-x1) ; where m is the slope, and (x1,y1) is a given point on the line • Slope-intercept: y=mx+b: where m is the slope and b is the intercept • Lines that coincide are the same line, but the equations may be written differently

  14. 3-6 Example Point Slope Form Slope-Intercept Form

More Related