I will try to explain today's class here but she said she will be after school and

lunch times there for questions.

--OK so let's start today's class with Geometric Mean, who can guess what it is

(so ms saatkamp:)

Geometric mean is for example:

x is the geometric mean Between a and b if:

See this order?! That is what means geometric mean,

if any other number was the geometric mean

it would be in those exact places.

Theorem 8-1:

If: you have a right triangle,

and the altitude from the right angle to the hypotenuse

Then: The 3 triangles are similar to each other

(Becareful with the order- ABC~ADB~BDC(all these are triangles)

Why? Take triangle ABD for example,

it has two angles congruent to the big triangle

So it is similar to the big triangle

Due to the same reason Triangle BDC is also similar to the big triangle

So if ABD~ABC and CDB~ABC you can say that

ABD~CBD by transitive property

Theorem 8-2:

If: you have a right triangle,
and the altitude from the right angle to the hypotenuse

READ THIS to understand the THEN part,

can you see that the altitude broke down the hypotenuse into 2 sides

keep thinking on them because

Then: The altitude is the geometric mean of those sides that

I made you think.

So... as BD is the Altitude the fraction will be like this:

Theorem 8-3:

If: you have a right triangle,

and the altitude from the right angle to the hypotenuse

To understand the THEN part choose one of the legs( I chose AB)

Then: The leg you choose is the geometric mean

So... :

HYP=Hypotenuse

COR=corresponding side(in this case AD)

Theorem 8-4: Pythegorean Theorem

(Same diagram from other theorems)

If: its a right triangle

Then: the HYP2(squared)= one leg2 plus the other leg2

Ms Saatkamp, proved this theorem in class and couldn't

do the proving here, because i'm having issues here with images and fractions

So if you want to know how to prove this ask her( sorry miss ¬¬)

Theorem 8-5: Converse of Pythagorean Theorem

(You can still use other theorem's diagrams)

If: The longest side squared is equal to one side squared plus the other squared

Then: It is a right triangle

The HomeWork is pg 401#15-32 all