1. Chapter 8 Section 1 Recall the rules for simplifying radicals:
(Similarity in Right Triangles)
Recall the rules for simplifying radicals:
No perfect square factor other than 1 is
allowed under the radical sign
No fraction is under the radical sign
No fraction has a radical in its
denominator

2. Simplify these radicals:

3. Simplify these radicals:

4. Recall our general proportion:
b & c are the means
If the means happen to be the same number…
That number is known as the geometric mean of
a and d. (If a, d, and x are all positive).

5. Examples: Find the geometric mean between 4 and 25
As a proportion it will look like…
Solving results in…

6. a b When the altitude is drawn to the hypotenuse of a right triangle,
the length of the altitude is the geometric
mean between the segments of the hypotenuse. a b

7. When the altitude is drawn to the hypotenuse of a right triangle,
each leg is the geometric mean between the
hypotenuse and the piece of the hypotenuse attached to it. a b c

8. When the altitude is drawn to the hypotenuse of a right triangle,
each leg is the geometric mean between the
hypotenuse and the piece of the hypotenuse attached to it. c a
leg 1 a b c

9. When the altitude is drawn to the hypotenuse of a right triangle,
each leg is the geometric mean between the
hypotenuse and the piece of the hypotenuse attached to it. c c b a
leg 2
leg 1 a b c

10. Ex. h E R J H 16 9 y x z x 16 y 25 z 25 9 x 9 y 16 z
x2 = 144
y2 = 225
z2 = 400
x = 12
y = 15
z = 20

11. Ex. i 2 4 y 5 z 5 x 2 1 y 4 z 4x = 4 y2 = 5 z2 = 20 x = 1 y = z = E RJ H 4 x y 2 z 2 4 y 5 z 5 x 2 1 y 4 z
4x = 4
y2 = 5
z2 = 20
x = 1
y =
z =

12. Ex. j x y
x + 7 12 z

13. Chapter 8 Section 1 Homework:
(Similarity in Right Triangles)
Homework:
Section 8.1 Written Exercises #1–39 (odds)
(exact answers only)