Monday, October 18, 2010

Geometry: Attack of the Vocab

Section 3-1 is all about terms.  Students need to feel confident with the following words:
  • Parallel
  • Perpendicular
  • Skew
  • Transversal
  • Corresonding Angles
  • Alternate Interior Angles
  • Alternate Exterior Angles
  • Same Side Interior Angles
Now it's really important to note that the pairs of angles apply to all cases when you've got two lines that are cut by a transversal.  The lines do NOT need to be parallel.


For additional help students may want to review these animations:
http://www.mathsisfun.com/geometry/alternate-interior-angles.html

Actually a little bit of googling brings up a lot of ideas and web definitions.  I encourage you guys to do some digging yourself and if you find a good online explanation, please share it in the comments (and yes there are Brownie Points for that).

Now to talk about Skew Lines as they are often the most confusing:

Imagine you've got two roads that run parallel, such as Maple and 14 mile road.  The two roads never intersect.  Now imagine you're driving down one and your friend is driving down the other.  You two are both running parallel each other.

Now a third friend starts driving up and down Haggerty.  Haggerty is at a right angle to them so your paths are perpendicular.  In fact if you time it right you'll both run into each other eventually, right?  There's an actual intersection of Maple and Haggerty (I think there's a Meijer there).

So suppose your third friend has a hover car and he can drive it like a normal car, but at 10 feet above the road.  He pulls up next to you and starts to over.  He decides he's going to drive with you along Maple.  Now you are both traveling along Parallel paths.  You're in the same direction and you'll never hit.  In fact your paths are Co-Planar (remember that word?).  You can imagine a big tarp between your car and the hover car.  Same path, same direction, just seperated by some distance.

Well what if your friend was hovering over Haggerty while you were driving on Maple?

Would his car ever hit yours?  Could it?  Of course not.  You're on the ground and he's hovering above you.  But! Your paths are not parallel.  Parallel requires the same direction, and to be coplanar.  By driving along Maple and him hovering over Haggerty, you two are not parallel but you will not intersect.  Hence your paths are Skew Lines.

The challenge of Skew Lines is that you have to think in 3 dimensions for them to make a lick of sense.  If you confine yourself to a flat piece of paper (a 2 D surface) you can't see them.  You see lines as parallel or intersecting.  But if you lift one line off the page and hover it over the page, you can create lines that are neither parallel, nor intersecting.  They are Skew.

Not S.P.E.W.  That's different.

(one BP to the first comment that identifies SPEW.)

2 comments:

  1. do we get any brownie points if we post a definition or example?? jw

    ReplyDelete