By: Crystal Page

• In this section you will learn about theorem
68 and learn how to apply this theorem in a multiple of different ways.

Leg
Leg
Altitude
Segment Segment
Hypotenuse

This Theorem has 3 important parts to it. Lets look at each part individually.
Part 1:
The altitude to the hypotenuse is the mean proportional between the segments of the hypotenuse.
In more simpler terms: You have a right triangle and there is a relationship between the segments and the altitude. seg 1
 alt alt seg 2 or a h
 h b

t
Part 2:
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 the leg.
g
Now this part sounds really confusing but it isn’t any harder.
hyp leg
 leg seg or m t
 t a or m
 g g b m

t
Part 3:
The product of the legs equals the product of the hypotenuse and the altitude to the hypotenuse.
g
This one is straight forward: leg 1
 leg 2
 hyp
 alt t
 g or
 h
 m m

Given: Diagram as marked
Find:m
Solution: Looking at the information given, you can see that the diagram gives you the length of two segments and an attitude. Ask yourself the question, “ which of the three methods learned uses segments and altitudes.” You will get the answer:
7
 m m 3
Cross multiplication seg 1
 alt alt seg 2
7

3
 m 2
21=m
2 m
 
21 Reject negative m

21

x
4
5
Start by setting up the proportion.
9
 x x 4
9

4
 x
2
36=x 2 Then
Given: Diagram as shown
Find: x
Look at the diagram. It uses a leg and either 2 segments or a hypotenuse. Ask yourself the question, “Which of the 3 methods learned uses a leg with segments or a hypotenuse. Your answer: hyp
 leg leg seg x x
 
 
6
36
Reject negative
X=6

3 a x
Given: Diagram as marked m
Find:x
In this diagram they give you 2 legs and you need to find the altitude. Right now you can’t use any method learned until you find the hypotenuse.
It’s a special right triangle: 3,4,5
Therefore the hypotenuse is 5 d
4
Now, we can use leg 1
 leg 2
3

4


5 x hyp
 alt
12=5x x

12
5

Now its your turn to try these new theorems by playing jeopardy with yourself. Just click on the value you want, in the category you want, to see the question.
(When you click on the category make sure you don’t click the number but just the box.)After deciding your answer,click the slide again and the answer will appear. Then, to return to the main Jeopardy page click the house.

Click Here to Begin the Game

Problems
100
200
Sample Problems
100
200
Sample
Problems
2
100
200
Random
100
200

leg 1 x leg 2= hyp x alt
What method would you use to find hyp ?
5
2
4

Seg1 over alt. = alt. Over seg2
What method would you use to find the alt.

2 x the sq. root of 7
x
11
4

Finals are worth 1/5 of your entire grade. They are important.
Why should you study for finals?

X=sq root of 15 y=4/5 times the sq root of 15 y
10 x
3
5
Solve for x and y

2 times the sq root of 35 x
7
20
Find x

(4.5, -3)
(0,5)
(0,-3)
4
Find the coordinates at A
9
A

Study a little bit each night. Don’t try to cram it all in the night before.
How should you study for finals?

"Geometry Worksheet." Tutor USA. 2008. Tutor. 29 May 2008
<http://www.tutor-USA.com/free-worksheets/geometry/right-triangle-similaritygeometric-mean.aspx>.
Rhoad, Richard. Geometry for Enjoyment and Challenge. Illinois: McDougal
Littell, 1997.