Mean Proportional – Day 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

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

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

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

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

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

Solve for the missing variable. Page 41 Solve for the missing variable. 𝑎 2 + 𝑏 2 = 𝑐 2 10 2 + 20 2 = 𝑐 2 100+400= 𝑐 2 500= 𝑐 2 500 = 𝑐 2 500 =𝑐 100∙5 =𝑐 10 5 =𝑐

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

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 12 2 + 4 3 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

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 5 2 + 55 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

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

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

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

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

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

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

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

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