1. Similar Figures, Scale Drawings, and Indirect Measure
More ways to use a ratio!!!!

2. Our Objectives?
We will use the skills practiced in solving proportions to find the missing value in similar figures.
We will apply the concepts of ratios to scale.
We will extend the idea of similar geometric shapes to find indirect measures.
We will start by applying the process to geometric shapes.

3. Looking back…..
Last year you discussed geometric shapes that were congruent and geometric shapes that were similar. Who remembers the difference?
Similar shapes have the same shape, but they are not the same size. The size is changed proportionately.
Congruent shapes have the same shape and same size.
This is the basis for the beginning of this lesson….

4. Do you know what corresponding parts are???????
Similar figures have two properties:
Corresponding sides are proportional
Corresponding angles are congruent
ABC ~ DEF Fill in information on your notes! D
53o
53o D
L A corresponds to L ___ A 9 6
L C corresponds to L ___ F E
90o
L B corresponds to L ___
90o B E __
AC corresponds to ___ __ DF 8 12 C
37o __ DE
37o __
AB corresponds to ___ F __
BC corresponds to ___ __ EF

5. I will choose to start with side AC and its corresponding side, DF
So….if the sides are proportional, then we should be able to write equal ratios from corresponding sides.
I will choose to start with side AC and its corresponding side, DF
Now I’ll go back to the small triangle and choose another side and its corresponding “partner.” D
53o
53o
90 = 90 A 9 6
10 15 =
6 9
90o
90o B E 8 12 C
37o
37o F
Use cross products to test for a proportion.
The sides of these similar triangles are proportional.
Notice the movement between the similar figures……..

6. Proportions are used to find missing sides in similar figures.24 16 n
Where you start doesn’t matter.
The pattern is what matters!
When setting up your proportion, think about a ping pong game between
corresponding sides.
Choose a starting place and ping-pong between the shapes to set up your ratios.
n _ = 16
24 = n 2 3 6
16(18) = 24 n
_____ ____
16(18) = n
12 = n

7. A
Pentagon ABCDE ~ Pentagon FGHIJ 12
E B F 6 ??
J G 14 ? 7
I H
D C 5 10
__ __
Find the length of sides JF and JI.
12 = ??
? = 5
(5)12 = 10n ??
____ _____
____ _____
(5)14 = 10n 2 2
6 = ??
7 = n

8. p
14 cm
8 cm
17 ½ cm n
10 cm
12 cm
21 cm
The two pentagons are similar. This means their sides are proportional, and their angles are congruent.
Let’s first find the length of side “n.” 7 4 2 1 7 4 5 2
p = 14 cm

9. Find the length of z.
If angle A is 35o, what is the
measure of angle R? 8 z
A R
The measure of angle R would also be 350
5_ = z__
____ ____
5(8) = 7z
5.71 = z (rounded)

10. This same process can be used to find indirect measurements
This same process can be used to find indirect measurements. Indirect measures are measures found using the idea of similar figures and corresponding sides
If we want to find the height of the tree, we can use the mailbox and shadow
to find this, using a proportion.
Imagine a triangle formed with each object. These triangles will be our similar shapes.

11. Choose the measures for your proportion
Choose the measures for your proportion. We want to find the height of the tree. A nearby mailbox that is 3 ft. tall has a shadow that is 2’ long. The tree’s shadow is 5ft. Long.
height.
3 ft.
5 _ = n_
2 ft.
5 ft.
Shadow is to shadow as
height is to height
_____ ______
(5)3 = 2n
7 ½ ft = height of the tree

12. Measurement Application
A rocket casts a shadow that is 91.5 feet long. A 4-foot model rocket casts a shadow that is 3 feet long. How tall is the rocket?
Write a proportion using corresponding sides. h 4 __
91.5 3
____ =
Write the equation and solve. 3h
____ _
4(91.5) =
122 = h
The rocket is 122 feet tall.

13. The Fried Bird 5 = 3 h 21 (21) 5 = 3 h 35 feet = h
On a sunny day, a telephone pole casts a shadow 21 ft long. A 5-foot-tall mailbox next to the pole casts a shadow 3 ft long. How tall is the pole?
5 = h 7 1
(21) 5 = 3 h h
5ft
21 ft ft.
_____ _____
35 feet = h

14. On a sunny afternoon, a goalpost casts a 75 ft shadow. A 6
On a sunny afternoon, a goalpost casts a 75 ft shadow. A 6.5 ft football player next to the goal post has a shadow 19.5 ft long. How tall is the goalpost?
h =
75(6.5) = 19.5h
____ ____ h
6.5 ft
75 ft ft.
25 feet = h

15. Using the same process, find the height
of this tree……
n_ = 10_
5(10) = 4 n
_____ ______
12 ½ ft. = height of the tree

16. Scale is another way to use proportions….
A scale drawing is an enlarged or reduced
drawing that is similar to an actual object
or place. The ratio of a scale (represented) distance to
actual distance is the scale.
The scale of a map is 1in. : 50 miles.
A map of Tennessee would show a distance of 3 ½ inches from
Nashville to Crossville. What is the actual distance between
these two cities? Complete this proportion in your notes to solve.
drawing
actual
1 in_ = ½ inches_
50 miles n miles
50(3.5) = 1 n
175 = miles

17. In this scale drawing of someone’s house, 1 cm = 12 ft
In this scale drawing of someone’s house, 1 cm = 12 ft. Find the actual dimensions of the living room and kitchen.
1.8 cm
Kitchen
1.5 cm
𝟐𝟏.𝟔 𝒇𝒕.
1 𝑐𝑚 12 𝑓𝑡 = 1.8 𝑐𝑚 ???
= 1.8(12) 1
18 𝒇𝒕.
1 𝑐𝑚 12 𝑓𝑡 = 1.5 𝑐𝑚 ???
= 1.5(12) 1
Living Room cm
2 cm
18 𝒇𝒕.
= 1.5(12) 1
𝟐𝟒 𝒇𝒕.
Drawing
actual
1 cm_ = _____ cm_
12 ft actual distance
1 𝑐𝑚 12 𝑓𝑡 = 1.5 𝑐𝑚 ???
Drawing
actual
1 cm_ = _____ cm_
12 ft actual distance
1 𝑐𝑚 12 𝑓𝑡 = 2 𝑐𝑚 ???
= 2(12) 1

18. Did we meet our objective of solving problems with proportions????