7.5 Using Proportionality Relationships

Warm-up7.5 Using Proportionality

Relationships

8 x

30 19

20

24

36

x

4 8

5

x2

6

A D

C

B

E

A. How are these ’s similar?

B. Write a similarity statement.

Lets Get Started!

C. Write the proportions and solve for x.

Let’s Explore!• ABC ~ MNO

• Find x • Find the similarity ratio of ABC : MNO• Complete the ratio • Observations?

Perimeter of ABCPerimeter of MNO

3

A

B C

M

N O8

x

16

Let’s Explore!• ABCD ~ MNOP

• Find x • Find the similarity ratio of ABCD : MNOP• Complete the ratio • Observations?

Perimeter of ABCDPerimeter of MNOP

6

A

B C

DM

N O

P

x

9

3

Let’s Explore!• ABC ~ MNO

• Find the similarity ratio of ABC : MNO• Complete the ratio • Observations?

Area of ABCArea of MNO

12

A

B C

M

N O9

16

12

h =6 h = 8

Let’s Explore!• ABCD ~ MNOP

• Find the similarity ratio of ABCD : MNOP• Complete the ratio • Observations?

Area of ABCDArea of MNOP

¼

A

B C

DM

N O

P

½

¾

1 ½

Solve: -Two similar triangles have side length in a ratio of 3ft:4ft. The perimeter of the smallest triangle is 96. Find the perimeter of the biggest triangle.

- Two rhombii have areas in the ratio of 121in2: 196in2

- what is the ratio of their perimeters?- what is the ratio of their side lengths?

Solve: - If the ratio of the perimeters of two pentagons is 5: 8 and the area of the smaller pentagon is 75cm2, what is the area of the larger pentagon?