Solving Similar Triangles

Learning Goals

By the end of the class I will be able to:

• Solve for the missing sides of similar triangles

Warm up

Which triangles are similar? How do you know?

a

b

c

d

30^o

40^o

60^o

50^o

It’s Not all about the angles

The angles are not all that make the triangles similar. The sides are also proportional:

ΔABC ~ ΔDEF

AB = BC = AC

DE EF DF

A

B

C

D

E

F

It’s Not all about the angles

ΔABC ~ ΔDEF

AB = BC = AC

DE EF DF

a = b = c

d e f

A

B

C

D

E

F

c

a

b

f

d

e

How Do we Use it?

1. Label your triangles

2. Set up your ratios

3. Substitute any information you have

c

a=

b=

f=

d

e=

12.5 cm

8 cm

16 cm

6.5 cm

a = b = c

d e f

16cm = 12.5 cm = c ⠀

d 8 cm 6.5cm

How Do we Use it?

4. Choose 1 of pair of ratios

5. Cross multiply

6. Finish solving

(divide by 12.5)

16cm = 12.5 cm = c ⠀

d 8 cm 6.5cm

16 x 8 = 12.5 x d

128 = 12.5 x d

10.24 cm = d

Let’s Practice

1. Label your triangles

2. Set up your ratios

3. Substitute any information you have

4. Choose 1 of pair of ratios

5. Cross multiply

6. Finish solving (divide)

4

9

y

p

12

10

x =

z =

m =

n =

x = y = z

m n p

4 = y = 9

10 12 p

4 = y

10 12

4 = 9

10 p

4(12) = (10)y

4(p) = 9(10)

48 = (10)y

4(p) = 90

4.8 = y

p = 22.5

Try it Yourself. Find all missing sides

1. Label your triangles

2. Set up your ratios

3. Substitute any information you have

4. Choose 1 of pair of ratios

5. Cross multiply

6. Finish solving (divide)

3

8

16

11

Try it Yourself. Find all missing sides

1. Label your triangles

2. Set up your ratios

3. Substitute any information you have

4. Choose 1 of pair of ratios

5. Cross multiply

6. Finish solving (divide)

5

5.5

15

21

Try it Yourself. Find all missing sides

1. Label your triangles

2. Set up your ratios

3. Substitute any information you have

4. Choose 1 of pair of ratios

5. Cross multiply

6. Finish solving (divide)

22

17

35

40