1. Geometry
8.1
Right Triangles

2. A radical is in simplest form when:
No perfect square factor other than 1 is under the radical sign.
No fraction is under the radical sign.
No radical is in a denominator.
#2 and #4 Together…You got the rest!!
Simplify:
Answers:

3. Geometric Mean If a, b and x are positive numbers and mean mean
then x is called the geometric mean between a and b.
Multiplying means/extremes we find that:
Taking the square root of each side:
A positive number

4. Geometric Mean
Basically, to find the geometric mean of 2 numbers, multiply them and take the square root. OR (add to notes: take the square root of each, then multiply try to find the geometric mean between 4 and 9 and the geometric mean between 36 and 50)
Note that the geometric mean always falls between the 2 numbers.
Ex: Find the geometric mean between 5 and 11.
Use the formula

5. Geometric Mean Ex: Find the geometric mean between the two numbers.
a. 5 and 20
Avoid multiplying large numbers together. Break numbers into perfect square factors to simplify.
b and 32

6. Directions: Find the geometric mean between the two numbers.
and 49
9. 1 and 3
and 6
and 24

7. Geometric Mean Find the geometric mean between the two numbers.
5 and 20
64 and 49
1 and 3
100 and 6
20 and 24

8. ∆ Review
Hypotenuse the side opposite the right angle in a right triangle
Altitude the perpendicular segment from a vertex to the line containing the opposite side

9. Theorem
If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. ~ a a ~ b b

10. Corollaries
When the altitude is drawn to the hypotenuse of a right triangle: Y
the length of the altitude is the geometric mean between the segments of the hypotenuse. X A Z
Each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg.

11. Corollary 1 = piece of hypotenuse altitude
altitude other piece of hypotenuse = Y X A Z

12. Corollary 2
hypotenuse leg
leg piece of hyp. adj. to leg = Y X A Z

13. Corollary 2
hypotenuse leg
leg piece of hyp. adj. to leg = Y X A Z

14. Directions: Exercises 24-31 refer to the diagram at right.
12. If CN = 8 and NB = 16, find AN.
13. If AN = 4 and CN = 12, find NB.
14. If AN = 4 and CN = 8, find AB.
15. If AB = and CB = 12, find NB.
16. If AC = 6 and AN = 4, find NB. N A C B

15. Homework
pg #16-30, odd

16. Exercises C 8 A x N 16 B
12. If CN = 8 and NB = 16, find AN. Let x = AN

17. Exercises C x A N B 8 12
14. If AN = 8 and NB = 12, find CN. Let x = CN

18. Exercises C 12 x A N B 18
17. If AB = 18 and CB = 12, find NB. Let x = NB

19. Answers Exercises 36 20
2√15 25 5