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f. f. d. d. c. c. a. a. b. b. e. e. Similar Figures & Scale Drawings.

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slide1

f

f

d

d

c

c

a

a

b

b

e

e

Similar Figures & Scale Drawings

These two triangles are called Similar Figures. 1. Why do you think that is true? 2. What do you think the words Similar Figures mean?

If side a was 5cm, side b was 3cm, side c was 8cm, and side d was 10cm, 3. Could you tell me the length of side e? 4. Could you tell me the length of side f?

10cm

8cm

5cm

3cm

You can find the answers because these Similar Figures are also in Proportion to each other, so you can use proportions to find your answers. Lets try it!

in your isn
In your ISN...
  • If the two triangles are similar, which side is congruent to
  • AB
  • BC
  • AC
slide6

How to use Proportions to find missing sides or numbers.

10cm

8cm

5cm

3cm

Divide with remaining number

=

Multiply across

f

6cm

N

Corresponding Sides

5cm

10cm

3cm

10cm

÷

5cm

=

N

3cm

N

N

Corresponding Sides

6cm

30cm

÷

5cm

=

5. What is the measure of the side f ?

6. Write out the proportion you used to find the missing measure for side f.

homework
Homework
  • Page 543
    • #1 - 14
slide10

2 inches

Bemidji Middle School

7 inches

Use the scale to find the actual size of the banner. ….(Hint- set up a proportion with similar labels instead of sides)

Scale Drawing is like Similar Figures except that you only see one of the similar figures. ( Ex. A State road map )-( The map gives you a scale measurement to help you determine the actual distance. 1inch : 3miles )

Scale 1 in : 3.5 ft

Model of the new School Banner

7 & 8. Set up and show the proportion and give the correct length in feet?

9 & 10. Set up and show the proportion and give the correct height in feet?

slide11

6-3 Homework “Scale Drawing & Similar Figures” Name:_________________ Hour: _____

Each pair of triangles is similar. Find the missing length. Round to the nearest tenth if necessary.

2 in.

1.

2.

x

y

10 in.

10 in.

3cm

4cm

12cm

4 in.

3.

4.

8 cm

z

6.4 cm

8 cm

30˚

30˚

7 cm

5 cm

a

7 cm

slide12

The scale of a map is 2 cm : 15 km. Find the actual distance for each map distance.

5. 6cm = _________km

6. 2.1 cm = _________km

8. 17.4 cm = _________km

7. 10 mm = _________km

The scale drawing has a scale of 1/2 in. : 10 ft. Find the length on the drawing for each actual length.

9. 40 ft = ________________in

10. 5 ft = __________________in

12. 3 1/2 ft = _______________in

11. 35 ft = _______________in

x 5

32 80

3 8

r 15

24 16

204 . c

13.

=

14.

=

15.

=

Solve Each Proportion.

slide13

Sample Problems

The scale of a map is 2 cm : 15 km. Find the actual distance for each map distance.

10 mm ? km

3 cm ? km

2 cm 15km

2 cm 15km

=

=

1. 3cm = _________km

2. 10 mm = _________km

x 5

15 25

3 4

r 7

24 16

204 . c

5.

=

6.

=

7.

=

3 • 15 ÷ 2 =

22.5

22.5 km

1 cm ? km

1 • 15 ÷ 2 =

7.5

7.5 km

The scale drawing has a scale of 1/2 in. : 10 ft. Find the length on the drawing for each actual length.

4

? in 80 ft

2 in

0.5 in 10 ft

0.5 • 80 ÷ 10 =

4

=

3. 80ft = ________________in

2.5

2.5 in

0.5 • 70 ÷ 10 =

2.5

? in 70 ft

0.5 in 10 ft

4. 70 ft = _______________in

=

Solve Each Proportion. **(Simplyify fraction and then solve.)

5 • 15 ÷ 25 = x

3 • 7 ÷ 4 = r

204 • 16 ÷ 24 = x