Mean Proportional – Day 2
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
27 9

the mean
Mean
Altitude
A
99 x
proportional
Propotional
27 x  81
27 27
x3
9
C x
D
Two parts of the
hypotenuse
27
B
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
4 xx

the mean
A
x 16
proportional
Mean
Leg
Propotional
x8
x
Lets try with
some values
Solve for x!
x 2  64
C
4 D
Corresponding
segment
12
hypotenuse
16
B
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
12 xx
the mean

proportional
A
xx 16
Mean
Leg
Propotional
x
x2 
x  64  3
x 8 3
Lets try with
some values
Solve for x!
C
4 D
12
hypotenuse
16
192
B
Corresponding
segment
Page 40
20
=
20
𝑥
20
=
20 25
25𝑥 = 400
25𝑥 400
=
25
25
𝑎2 + 𝑏 2 = 𝑐 2
202 + 𝑦 2 = 252
400 + 𝑦 2 = 625
−400
− 400
𝑦 2 = 225
𝑦2
= 225
𝑦
𝑥
𝑦 = 15
𝑥 = 16
Mean proportional
Page 40
Solve for the missing variable.
32
=
32
15 32
=
32
𝑥
15𝑥 = 1024
15𝑥 1024
=
15
15
𝑥 = 68.26
Page 40
Solve for the missing variable.
12
7.2
𝑤
=
12
𝑤
12
=
12 20
20𝑤 = 144
20𝑤 144
=
20
20
𝑤 = 7.2
𝑎2 + 𝑏 2 = 𝑐 2
𝑥 2 + 7.22 = 122
𝑥 2 + 51.84 = 144
−51.84 − 51.84
𝑥 2 = 92.16
𝑥 2 = 92.16
𝑥 = 9.6
Page 41
Solve for the missing variable.
𝑎2 + 𝑏 2 = 𝑐 2
102 + 202 = 𝑐 2
100 + 400 = 𝑐 2
500 = 𝑐 2
500 =
500 = 𝑐
100 ∙ 5 = 𝑐
10 5 = 𝑐
𝑐2
What kind of special right triangle is
the biggest triangle?
Solve for x and y
6
6 3
6: 6 3: 12
30: 60: 90
𝑎2 + 𝑏 2 = 𝑐 2
𝑦 2 + 6 = 122
12
𝑥
=
𝑥
3
𝑥
=
𝑥 12
𝑦 2 + 36 = 144
−36 − 36
𝑥 2 = 36
𝑦 2 = 108
𝑥 2 = 36
𝑦 2 = 108
𝑥=6
𝑦 = 108
𝑦 = 36 ∙ 3
𝑦=6 3
Page 42
Solve for x and y
4 3
𝑎2 + 𝑏 2 = 𝑐 2
122
𝑦
=
𝑦
4
𝑦
=
𝑦 12
𝑦 2 = 48
𝑦 2 = 48
+ 4 3
2
= 𝑐2
144 + 48 = 𝑐 2
𝑦 = 16 ∙ 3
196 = 𝑐 2
𝑦=4 3
196 =
14 = 𝑐
𝑐2
Page 42
Solve for x and y
𝑦
=
𝑦
5
𝑦
=
𝑦 11
55
𝑦2
= 55
𝑦 2 = 55
𝑦 = 55
4 5
𝑎2 + 𝑏 2 = 𝑐 2
52
+
55
2
= 𝑐2
25 + 55 = 𝑐 2
80 = 𝑐 2
80 =
16 ∙ 5 = 𝑐
4 5=𝑐
𝑐2
Homework
Page
43
#12,13,14,16,18,19,20
Separate Sheet
Page 43
4
4
=
4
𝑥 4
=
4 8
8𝑥 = 16
8𝑥 16
=
8
8
𝑥
8
𝑥=2
Page 43
10
10
=
10
𝑥
10
=
10
5
5
5𝑥 = 100
5𝑥 100
=
5
5
𝑥
𝑥 = 20
Page 43
6
6
=
6
𝑥 6
=
6 9
9𝑥 = 36
9𝑥 36
=
9
9
𝑥
9
𝑥=4
Page 43
10
10
=
10
𝑥
10
=
10
4
4
𝑥
4𝑥 = 100
4𝑥 100
=
4
4
𝑥 = 25
Page 43
𝑥
𝑥
=
𝑥
18 𝑥
=
𝑥
2
2
𝑥 2 = 36
18
𝑥 2 = 36
𝑥=6
Page 43
𝑥
𝑥
=
𝑥
18 𝑥
=
𝑥
8
8
18
𝑥 2 = 144
𝑥 2 = 144
𝑥 = 12
Page 43
𝑥
𝑥
=
𝑥
12 𝑥
=
𝑥
3
3
9
𝑥 2 = 36
𝑥 2 = 36
12
𝑥=6