Chapter 3 : Lines and Angles

Let's not limit ourselves to FLAT, Planar thinking.  Two lines that exist in space may intersect or they may not.  Let's take a look.

Math World provides us with a great 3-D figure of Skew Lines.  Check it out.

Math World provides us with a great 3-D figure of parallel lines.  Check it out.

When 2 lines do intersect, those lines are coplanar and angles are formed.  Lets talk about angles

Intersecting lines do not necessarily intersect at 90 degrees.

Try this applet to see what happens to two lines on the coordinate plane.

You should already be familiar with classifications of some angle pairs like the ones below.

At Saltire's web site you'll be able to see for yourself what happens to the angles as the lines are changed.

vertical angles

We're more interested in cases where more than 2 lines are involved

Hamilton's math page will give you a good idea where we're going with this.

Math .com gives a great tutorial of intersecting lines and angle relationships.

We can use one Postulate to prove many theorems about two parallel lines and a transversal.

Can you determine which pairs of angles are Corresponding Angles.?

The angles in the grey area are Interior Angles and angles A, B, H, and G are the Exterior Angles

We'll solve problems with parallel lines and transversals in the coordinate plane.  Do you remember how to write the equation of line with a given slope and point.

Given:  2 Lines in the coordinate plane.  Determine if they are parallel by finding the slope.

Challenge: a. Find the Distance from a point to a line b. Find the Distance between 2 parallel        lines

Challenge Hint.  Draw a line perpendicular to the two lines. find the points of intersection, and use the distance formula.

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