1. Use Similar Right Triangles
Ch 7.3

2. Similar Right Triangle Theorem
If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original right triangle.

3. Name 3 similar triangles?
1. Draw the smallest triangle.
2. Draw the middle triangle.
3. Draw the largest triangle.
4. Match up the angles.
îSUT ~ îTUR
~ îSTR

4. Name the similar triangles, then find x.
îEHG ~ îGHF ~ îEGF
To find x make a ratio of the hypotenuses and the a ratio of 2 proportional legs.

5. Name the similar triangles and find x.
îLKM ~ îMKJ ~ îLMJ

6. Find x and y. 72 21 y x

7. Find x.

8. Find x

9. Geometric Mean Altitude Theorem
In a right triangle the altitude from the right angle to the hypotenuse divides the hypotenuse into 2 segments.
The length of the altitude is the geometric mean of the lengths of the 2 segments

12. Finding the length of the altitude
Set up a proportion to find BD. B C A D
Find side AD.
Plug values into

13. Find the amplitude, if these are right triangles
Find the amplitude, if these are right triangles. One of these is not a right triangle 1. 2.
8.5
6.6 3.
not right

14. Geometric Mean (Leg) Theorem
In a right triangle, the altitude divides the hypotenuse into 2 segments.
The length of each leg of each right triangle is the geometric mean of length of the hypotenuse and a segment of the hypotenuse

15. Find x and y y x
12.75
4.25

16. Find x

17. Find x and y y
x +2 8 2

18. Find a

19. Find b

21. Find x and y 30 16 z x y
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