Section 9.3

Today we learned about the Altitude-on-Hypotenuse theorems. In the first diagram of the picture above, you see a proof. This is proving the statement: if you draw a right triangle, and you draw altitude to hypotenuse, you create three similar right triangles.

You may now use this statement in your future proofs! YAY! :D
http://www.youtube.com/watch?v=KzBT8130TqU <-- this video shows you the different ways you can create these right triangles, changing the size's of the triangle. :)

http://www.youtube.com/watch?v=tuAjSiuG8j0
Watch it. Wait until after the advertisement. It's worth it...

OKAY. About the next diagram. This shows a right triangle with the altitude, the triangles next to it are the similar triangles formed by the altitude. There are many rules that ALWAYS apply to triangles under the "pink" rule (a.k.a the rule above in pink) These rules that are always true are in ORANGE.

You may notice there are also side lengths, found in the ratios, that are highlighted in blue. This was done NOT ONLY to *try* and make the diagram as cool as Mr. Wilhelm's, but for a learning stand point.


Highlighted in blue are the geometric means. This is relevant to Theorem 68- which, in short, says; The altitude to the hypotenuse is the mean proportional between segments of the hypotenuse.

The theorem also states; Either leg of the given right triangle is the mean proportional between the hypotenuse of the given right triangle and the segment of the hypotenuse adjacent to that leg.


(PS CLICK ON THE PICTURE, IT MAKES IT EASIER TO SEE!)

Hope you enjoy this, I tried. Failed, but ... "It is hard to fail, but it is worse never to have tried to succeed" Words of wisdom. :)

-Maggie Ridenour