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?– 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:

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?

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

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?

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?

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

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

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

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:

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?

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

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?

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

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?

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

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?

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

Theorems