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Note-taking Guide
• I suggest only taking writing down things in red
• If there is a diagram you should draw, it will be indicated
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Chapter 3
Parallel and Perpendicular Lines
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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:
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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?
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Section 3.1 – Identify Pairs of Lines and Angles
Example problems:1. Determine the line(s)
that are parallel to
2. Determine the line(s) that are skew to
3. Determine the lines that intersect
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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?
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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?
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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
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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
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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
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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:
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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?
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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
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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?
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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
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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?
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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
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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?
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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
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Theorems