1 / 20

Note-taking Guide

Note-taking Guide. I suggest only taking writing down things in red If there is a diagram you should draw, it will be indicated. Chapter 3. Parallel and Perpendicular Lines. Section 3.1 – Identify Pairs of Lines and Angles. What does it mean for lines to be parallel ?

keona
Download Presentation

Note-taking Guide

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. Note-taking Guide • I suggest only taking writing down things in red • If there is a diagram you should draw, it will be indicated

  2. Chapter 3 Parallel and Perpendicular Lines

  3. Section 3.1 – Identify Pairs of Lines and Angles • What does it mean for lines to be parallel? • Lines never intersect • Lines are coplanar • Notice that and are both IN Plane A • Symbols for parallel: • On a diagram: little arrows in the middle of the lines (notice how the lines in this diagram have one little arrow) • In a statement:

  4. Section 3.1 – Identify Pairs of Lines and Angles • What if the lines never intersect, but are not in the same plane? • These are called skew lines • In the diagram and are skew • Can you name another example of skew lines in the diagram?

  5. Section 3.1 – Identify Pairs of Lines and Angles Example problems: • Determine the line(s) that are parallel to • Determine the line(s) that are skew to • Determine the lines that intersect

  6. Section 3.1 – Identify Pairs of Lines and Angles • Parallel Planes • Planes that never intersect • For example, plane DCF and plane ABG are parallel • Can you name another pair of parallel planes?

  7. Section 3.1 – Identify Pairs of Lines and Angles • On a sheet of paper, draw a line and label it as m. • Add a point not on the line and label it as P • Draw as many lines through point P that are parallel to line m as you can • How many lines were you able to draw? • Now draw as many lines through point P that are perpendicular to line m as you can • How many lines were you able to draw?

  8. Section 3.1 – Identify Pairs of Lines and Angles • Could you prove that there is only one line parallel to m through P? • Could you prove that there is only one line perpendicular to m through P? • As it turns out, you cannot prove either of these because they are postulates • Put the things on the right on your Postulates sheet • Postulate 13 – Parallel PostulateIf there is a line and a point not on the line, then there is exactly one line through the point to the line • Postulate 14 – Perpendicular PostulateIf there is a line and a point not on the line, then there is exactly one line through the point to the line

  9. Section 3.1 – Identify Pairs of Lines and Angles • Transversal • A line that intersects two (or more) coplanar lines at different points • Line is a transversal because it crosses line and line at different points • Note-taking guide: you should draw this diagram

  10. Section 3.1 – Identify Pairs of Lines and Angles Special names of pairs of angles formed by a transversal: • Corresponding: • Same direction from intersection point

  11. Section 3.1 – Identify Pairs of Lines and Angles Special names of pairs of angles formed by a transversal: • Corresponding: • Same direction from intersection point • (Add the numbers on your diagram) • Ex:

  12. Section 3.1 – Identify Pairs of Lines and Angles Special names of pairs of angles formed by a transversal: • Corresponding: • Same direction from intersection point • (Add the numbers on your diagram) • Ex: • Can you name another pair of corresponding angles?

  13. Section 3.1 – Identify Pairs of Lines and Angles Special names of pairs of angles formed by a transversal: • Alternate Interior: on opposite (alternate) sides of the transversal in between the two lines

  14. Section 3.1 – Identify Pairs of Lines and Angles Special names of pairs of angles formed by a transversal: • Alternate Interior: on opposite (alternate) sides of the transversal in between the two lines • Ex: • Name another pair?

  15. Section 3.1 – Identify Pairs of Lines and Angles Special names of pairs of angles formed by a transversal: • Alternate Exterior: on opposite (alternate) sides of the transversal outside the two lines

  16. Section 3.1 – Identify Pairs of Lines and Angles Special names of pairs of angles formed by a transversal: • Alternate Exterior: on opposite (alternate) sides of the transversal outside the two lines • Ex: • Name another pair?

  17. Section 3.1 – Identify Pairs of Lines and Angles Special names of pairs of angles formed by a transversal: • Consecutive Interior: on the same side of transversal in between the lines

  18. Section 3.1 – Identify Pairs of Lines and Angles Special names of pairs of angles formed by a transversal: • Consecutive Interior: on the same side of transversal in between the lines • Ex: • Name another pair?

  19. Section 3.2 – Use Parallel Lines and Transversals Postulate 15: Corresponding Angles Postulate If two parallel lines are cut by a transversal, the pairs of corresponding angles are congruent

  20. Theorems

More Related