1. Mean Proportional

2. Means and Extremes
In a proportion, the product of the means is equal to the product of the extremes
Means
Extremes

3. Mean Proportional
If the two means of the proportional are equal , it is called the mean proportional between the first and fourth terms.
In the proportion
the mean proportional is?
The mean proportional is also known as the geometric mean

4. Mean Proportional Page 38
Which of the following represents the geometric mean of 4 and 9?
(1) 6 (3) 18
(2) 6.5 (4) 36
4 𝑥 = 𝑥 9
𝑥=±6
𝑥=6
𝑥 2 =36
𝑥 2 = 36
3. 8 is the geometric mean between 4 and which of the following values?
(1) 64 (3) 16
(2) 24 (4) 4
4 8 = 8 𝑥
4𝑥 4 = 64 4
4𝑥=64
𝑥=16

5. Page 39
Theorems
Right Triangle Altitude Theorem – If the altitude of a right triangle is drawn (to the hypotenuse), then it divides the triangle into two similar triangles that are similar to the original. A C D B

6. Start by filling in the mean proportional
Page 39
Theorems
Mean proportionality theorem – The altitude of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.
Start by filling in the mean proportional
Altitude
Mean Propotional A
Lets try with some values
Solve for x! 9 C x D 27 B
Two parts of the hypotenuse

7. Page 39
Notice that we did not have the ± in front of our answer this time. Why?
6 𝑥 = 𝑥 3
𝑥= 9∙2
𝑥=3 2
𝑥 2 =18
𝑥 2 = 18

8. 4 𝑥 = 𝑥 9
𝑥 2 =36
𝑥 2 = 36
𝑥=6

9. Page 40
18 𝑥+9 = 𝑥+9 8
𝑥+9 𝑥+9 =144
𝑥 2 +9𝑥+9𝑥+81=144
𝑥 2 +18𝑥+81=144
−144−144
𝑥 2 +18𝑥−63=0
𝑥+21 𝑥−3 =0
𝑥+21=0
𝑥−3=0
𝑥=−21
𝑥=3
REJECT

10. Page 43
9 12 = 12 𝑥 12
9𝑥=144
9𝑥 9 = 144 9 9 𝑥
𝑥=16

11. Page 43
4 8 = 8 𝑥 8
4𝑥=64
4𝑥 4 = 64 4 4 𝑥
𝑥=16

12. Homework
Page 43
#11,15,17,21,22,23
Separate Sheet

13. Page 43
3 6 = 6 𝑥 6
3𝑥=36
3𝑥 3 = 36 3 3 𝑥
𝑥=12

14. Page 43
4 𝑥 = 𝑥 9 𝑥
𝑥 2 =36
𝑥 2 = 36 4 9
𝑥=6

15. Page 43
3 𝑥 = 𝑥 27 𝑥
𝑥 2 =81
𝑥 2 = 81 3 27
𝑥=9

16. Page 43
5 𝑥 = 𝑥 20
𝑥 2 =100 𝑥
𝑥 2 = 100
𝑥=10 5 20

17. Page 43
2 8 = 8 𝑥 8
2𝑥=64
2𝑥 2 = 64 2 2 𝑥
𝑥=32

18. Page 43
𝑥 6 = 6 9𝑥
9𝑥 2 =36 6
9𝑥 2 9 = 36 9
𝑥 2 =4 𝑥 9𝑥
𝑥 2 = 4
𝑥=2
9𝑥=2∙9=18
𝑥=2