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

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

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: 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 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: Consecutive Interior: on the same side of transversal in between the lines

Section 3.1 – Identify Pairs of Lines and Angles

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