mean proportional – day 2. theorems - review page 39 mean proportionality theorem – the altitude...
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Mean Proportional – Day 2
Theorems - Review
Page 39
Mean proportionality theorem – The altitude of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.
A
C BD
AltitudeMean Propotional
Two parts of the hypotenuse
9
x 27
9
9x
9
9
27
8127 x27 27
3x
Start by filling in the mean
proportional
Theorems - Review
Page 39
Leg Proportional Theorem: Each leg of a right triangle is the mean proportional between the hypotenuse and the corresponding segment of the hypotenuse
A
C BD
LegMean Propotional
hypotenuse
x
4 12
x
x
16
4 x
x
64 2 x
8x
Start by filling in the mean
proportional
Lets try with some values
Solve for x!
Corresponding segment
16
4
Leg Proportional Theorem
Page 39
Leg Proportional Theorem: Each leg of a right triangle is the mean proportional between the hypotenuse and the corresponding segment of the hypotenuse
A
C BD
LegMean Propotional
hypotenuse
x
12
x
x
16
12 x
x
921 2 x
364 x
Start by filling in the mean
proportional
Lets try with some values
Solve for x!
Corresponding segment
16
38x
Page 40
𝑥
Hypotenuse
Mean proportional
❑20
=20❑
𝑥20
=2025
25 𝑥=40025𝑥25
=40025
𝑥=16
𝑦
𝑎2+𝑏2=𝑐2
202+𝑦2=252
4 00+𝑦2=625−400−400
𝑦 2=225
√𝑦 2=√225𝑦=15
Solve for the missing variable.
Page 40
❑32
=32❑
1532
=32𝑥
15 𝑥=102415𝑥15
=102415
𝑥=68.26
Page 40
Solve for the missing variable.
❑12
=12❑
𝑤12
=1220
20𝑤=14420𝑤20
=14420
𝑤=7.2
𝑤7.2
𝑎2+𝑏2=𝑐2
𝑥2+7.22=122
𝑥2+51.84=144−51.84−51.84
𝑥2=92.16
√𝑥2=√92.16𝑥=9.6
Solve for the missing variable.
Page 41
𝑎2+𝑏2=𝑐2
102+202=𝑐2
100+400=𝑐2
5 00=𝑐2
√500=√𝑐2
√500=𝑐√100 ∙5=𝑐
10√5=𝑐
Solve for x and y
12
❑𝑥
=𝑥❑
3𝑥
=𝑥12
𝑥2=36
√𝑥2=√36𝑥=6
6
𝑎2+𝑏2=𝑐2
𝑦 2+6=122
𝑦 2+36=144−36−36𝑦 2=108
√𝑦 2=√108
𝑦=√108𝑦=√36 ∙3
𝑦=6 √3
6 √3
What kind of special right triangle is the biggest triangle?
6 :6 √3 :12 30 :60 : 90
Solve for x and y Page 42
❑𝑦
=𝑦❑
4𝑦
=𝑦12
𝑦 2=48
√𝑦 2=√ 48
𝑦=√16 ∙3𝑦=4√3
4√3
𝑎2+𝑏2=𝑐2
122+( 4 √3 )2=𝑐2
144+48=𝑐2
1 96=𝑐2
√196=√𝑐2
1 4=𝑐
Solve for x and y
❑𝑦
=𝑦❑
5𝑦
=𝑦11
𝑦 2=55
√𝑦 2=√55𝑦=√55
√55
𝑎2+𝑏2=𝑐2
52+ (√55 )2=𝑐2
25+55=𝑐2
8 0=𝑐2
√80=√𝑐2
√16 ∙5=𝑐4√5=𝑐4√5
Page 42
Homework
Page 43#12,13,14,16,18,19,20
Separate Sheet
Page 43
8
4
𝑥
❑4
=4❑
𝑥4=
48
8 𝑥=168 𝑥8
=168
𝑥=2
Page 43
10
5
𝑥
❑10
=10❑
𝑥10
=105
5 𝑥=1005𝑥5
=1005
𝑥=20
Page 43
6
9
𝑥
❑6
=6❑
𝑥6=
69
9 𝑥=369𝑥9
=369
𝑥=4
Page 43
4
10
𝑥
❑10
=10❑
𝑥10
=104
4 𝑥=1004 𝑥4
=1004
𝑥=25
Page 43
2
𝑥
18
❑𝑥
=𝑥❑
18𝑥
=𝑥2
𝑥2=36
√𝑥2=√36
𝑥=6
Page 43
8
𝑥
18
❑𝑥
=𝑥❑
18𝑥
=𝑥8
𝑥2=144
√𝑥2=√144
𝑥=12
Page 43
3
𝑥
9
❑𝑥
=𝑥❑
12𝑥
=𝑥3
𝑥2=36
√𝑥2=√36
𝑥=612