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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 ?

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Note-taking Guide

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  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

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