8.2 Problem Solving in Geometry with Proportions

Additional Properties of Proportions

If , then

If , then

d

c

b

a

d

b

c

a

d

dc

b

ba

d

c

b

a

Using Properties of Proportions

Tell whether the statement is true.

4

3

3

3,43

5

3,

106

cathen

caIf

r

pthen

rpIf true

Not true—c + 3 should be c + 4.

In the diagram .

Find the length of BD.CE

AC

BD

AB

A

C

E

B

D

x 10

16 30AB = AC 16 = 20*BD CE X 10

160 = 20X 8 = X

• Find the length of AC by• Subtracting 10 from 20.

In the diagram Solve for DE.

A

B

C

D

E

2

3

5

DE

AD

BC

AB

2 = 53 X

15 = 2x7.5 = x

Geometric mean

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.

8(18) = 144

√144 = 12

b

x

x

a

Geometric Mean

Find the geometric mean of 5 and 20.

The geometric mean of x and 5 is 15. Find the value of x.

So, the square root of 5x = 15So, 152 = 5x 225 = 5x 45 = x

Different perspective of Geometric mean

The geometric mean of ‘a’ and ‘b’ is √ab

Therefore geometric mean of 4 and 9 is 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

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?

length widthScale Model = 107.5 = 11.25Actual Titanic 882.75 x

107.5x = 9930.9375 x ≈ 92.38

Homework

8.2 P. 468-471 10-28E 29-33All 38-40 All 44-46 All