8.2 Problem Solving in Geometry with Proportions

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8.2 Problem Solving in Geometry with Proportions. Warm-Up. 1) ∆ ABC ≅ ∆ HIJ. Name three pairs of congruent sides. 2) Solve each proportion. a) 3 = x b) 2 = 8 c) x = 1 4 8 x 24 9 3. ?s. Additional Properties of Proportions. If , then

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### 8.2 Problem Solving in Geometry with Proportions

Warm-Up
• 1) ∆ ABC ≅∆HIJ. Name three pairs of congruent sides.
• 2) Solve each proportion.
• a) 3 = x b) 2 = 8 c) x = 1

4 8 x 24 9 3

Using Properties of Proportions
• Tell whether the statement is true.
In the diagram .

Find the length of BD.

A

30

16

B

C

x

10

D

E

In the diagram
• Solve for DE.

A

5

2

D

B

3

E

C

Practice
• P. 468-470 #9-16, 23-28, 33, 34
Dilations
• Dilation—transformation wherein the figure is enlarged or reduced by a set amount
• The amount is referred to as the scale factor

6

3

a) Identify the Dilation b) Find the scale factor c) Solve for the variables

A 25 B

A’ B’

x 8 8 y

C’ D’

10

C z D

10

Practice
• P. 509-511 #8-10, 20-21
Warm-Up
• 1) Identify the dilation and find the scale factor. Then, find the values of the variables.
• 2) Find the measures of the angles:

M

M’

x

18

Q’

12

Q

20

y

15

N’

V

N

61°

U

W

58°

X

It’s Lean, It’s Green, It’s…
• The geometric mean of two positive numbers a and b is the positive number x such that
• Find the geometric mean of 8 and 18.
• Solution: 12
Quick Practice
• Find the geometric mean of 5 and 20.
• The geometric mean of x and 5 is 15. Find the value of x.
Another Way to Solve
• The geometric mean of ‘a’ and ‘b’ is √ab
• Using this method, find the geometric mean of 4 and 9
• Solution: 6, since √(4*9) = √36 = 6.
Geometric mean
• Find the geometric mean of the two numbers.
• 3 and 27

√(3)(27) = √81 = 9

• 4 and 16

√(4)(16) = √64 = 8

• 5 and 15

√(5)(15) = √75 = 5√3

More Practice
• Find the geometric mean of…
• 1) 7 and 63
• 2) 5 and 11
• 3) 10 and 7
A scale model of the Titanic is 107.5 inches long and 11.25 inches wide. The titanic itself was 882.75ft long. How wide was it?