Sections 9.6 & 9.7

Hello everyone!
Today we covered two sections, 9.6 & 9.7
Lets start with 9.6
9.6 was a pretty short, simple section about families of right triangles and Pythagorean Triples.
A Pythagorean Triple is any three whole numbers that satisfy the Pythagorean theorem,
For example, 3,4,and 5 are Pythagorean triples. Also, 8, 15, and 17

Any multiples of these are also in the same family of right triangles. For example 6, 8, and 10. These are all multiples of 3,4,and 5, therefore they are in the same family.



Next, is section 9.7

Section 9.7 has some shortcuts when dealing with "special" right triangles.

The first trick is for dealing with right triangles that have angle measures of 30°, 60°, and 90°.

Let a represent the side length of the short leg of the triangle. The hypotenuse is 2a. The long leg is a

For example, in the picture to the left, if a=4, the hypotenuse=8, and the long leg=4.

If you are slightly confused, I found that drawing an equilateral triangle and then drawing an altitude showed the relationships more clearly. The video below shows how to do this.

The video was giving me a little trouble so if it doesn't work here's the link

http://www.youtube.com/watch?v=_eBIuP9pugM

The next shortcut is for isosceles right triangles. These triangles have angle measures of 45°, 45°, and 90°. Let a represent the side length of the leg. Because it's isosceles the other leg is also a. The hypotenuse however, is a.

That wraps up sections 9.6 and 9.7. They were short and relatively easy sections. Personally I would prefer if our math homework looked like this

If only,

Ryan