1. Mean Proportional – Day 2

2. Start by filling in the mean proportional
Page 39
Theorems - Review
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 9 C B x D 27
Two parts of the hypotenuse

3. Start by filling in the mean proportional
Page 39
Theorems - Review
Leg Proportional Theorem: Each leg of a right triangle is the mean proportional between the hypotenuse and the corresponding segment of the hypotenuse
Start by filling in the mean proportional A
Mean Propotional
Leg x
Lets try with some values
Solve for x! C 4 B D 12
hypotenuse 16
Corresponding segment

4. Start by filling in the mean proportional
Page 39
Leg Proportional Theorem
Leg Proportional Theorem: Each leg of a right triangle is the mean proportional between the hypotenuse and the corresponding segment of the hypotenuse
Start by filling in the mean proportional A
Mean Propotional
Leg x
Lets try with some values
Solve for x! C 4 B D 12
hypotenuse 16
Corresponding segment

5. Page 40
20 = 20
𝑎 2 + 𝑏 2 = 𝑐 2
𝑦 2 = 25 2
𝑥 20 = 20 25
400+ 𝑦 2 =625
Hypotenuse
− −400
𝑦 2 =225 𝑦
25𝑥=400 𝑥
25𝑥 25 =
𝑦 2 = 225
𝑦=15
𝑥=16
Mean proportional

6. Solve for the missing variable.
Page 40
Solve for the missing variable.
32 = 32
15 32 = 32 𝑥
15𝑥=1024
15𝑥 15 =
𝑥=68.26

7. Solve for the missing variable.
Page 40
Solve for the missing variable.
12 = 12
𝑎 2 + 𝑏 2 = 𝑐 2
𝑥 = 12 2
7.2 𝑤
𝑤 12 = 12 20
𝑥 =144
− −51.84
20𝑤=144
𝑥 2 =92.16
20𝑤 20 =
𝑥 2 =
𝑥=9.6
𝑤=7.2

8. Solve for the missing variable.
Page 41
Solve for the missing variable.
𝑎 2 + 𝑏 2 = 𝑐 2
= 𝑐 2
= 𝑐 2
500= 𝑐 2
500 = 𝑐 2
500 =𝑐
100∙5 =𝑐
10 5 =𝑐

9. Solve for x and y 6:6 3 :12 30:60:90 6 3 6 𝑎 2 + 𝑏 2 = 𝑐 2
What kind of special right triangle is the biggest triangle?
6:6 3 :12
30:60:90
6 3 6
𝑎 2 + 𝑏 2 = 𝑐 2
𝑦 2 +6= 12 2 12
𝑦 2 +36=144
−36 −36
𝑥 = 𝑥
𝑥 2 =36
𝑦 2 =108
𝑥 2 = 36
𝑦 2 = 108
3 𝑥 = 𝑥 12
𝑥=6
𝑦= 108
𝑦= 36∙3
𝑦=6 3

10. Solve for x and y 4 3 𝑎 2 + 𝑏 2 = 𝑐 2 12 2 + 4 3 2 = 𝑐 2 144+48= 𝑐 2
Page 42
4 3
𝑎 2 + 𝑏 2 = 𝑐 2
= 𝑐 2
144+48= 𝑐 2
𝑦 = 𝑦
𝑦= 16∙3
196= 𝑐 2
196 = 𝑐 2
𝑦=4 3
4 𝑦 = 𝑦 12
14=𝑐
𝑦 2 =48
𝑦 2 = 48

11. Solve for x and y 𝑦 = 𝑦 𝑎 2 + 𝑏 2 = 𝑐 2 5 2 + 55 2 = 𝑐 2 5 𝑦 = 𝑦 11
Page 42
Solve for x and y
𝑦 = 𝑦
𝑎 2 + 𝑏 2 = 𝑐 2
= 𝑐 2
5 𝑦 = 𝑦 11
25+55= 𝑐 2
80= 𝑐 2
𝑦 2 =55 55
80 = 𝑐 2
𝑦 2 = 55
16∙5 =𝑐
𝑦= 55
4 5 =𝑐
4 5

12. Homework
Page 43
#12,13,14,16,18,19,20
Separate Sheet

13. Page 43
4 = 4 4
𝑥 4 = 4 8 𝑥
8𝑥=16
8𝑥 8 = 16 8 8
𝑥=2

14. Page 43
10 = 10 10
𝑥 10 = 10 5 5
5𝑥=100
5𝑥 5 = 100 5 𝑥
𝑥=20

15. Page 43
6 = 6 6
𝑥 6 = 6 9 𝑥
9𝑥=36
9𝑥 9 = 36 9 9
𝑥=4

16. Page 43
10 = 10 10
𝑥 10 = 10 4 4
4𝑥=100
4𝑥 4 = 100 4 𝑥
𝑥=25

17. Page 43
𝑥 = 𝑥 𝑥
18 𝑥 = 𝑥 2 2
𝑥 2 =36
𝑥 2 = 36 18
𝑥=6

18. Page 43
𝑥 = 𝑥 𝑥
18 𝑥 = 𝑥 8 8
𝑥 2 =144
𝑥 2 = 144 18
𝑥=12

19. Page 43
𝑥 = 𝑥 𝑥
12 𝑥 = 𝑥 3
𝑥 2 =36 3 9
𝑥 2 = 36 12
𝑥=6