REVIEW – CHAPTER 4 & 5
Stretching & Shrinking
By: Ms. D. Kritikos
Similar Figures
 Polygons
that have the same shape are similar.
Similar figures must have:
 Corresponding
angles that are congruent
 Corresponding sides that have SCALE FACTOR (ratio
of the lengths are proportional)
The triangles below are similar. Find
the missing measurements.
a
3
2.75
a = _____
8
b
11
b = _____
16
24
c
c = _____
There are 2 different ways to solve
this problem:

FIRST WAY, by using Scale Factor:
 Find 2 corresponding sides in similar figures where
both measurements are know.
 Divide the larger number by the smaller number.
 Find the corresponding side to the unknown
measurement; if the smaller number is known,
multiply it by the scale factor. If the larger number is
known, divide it by the scale factor.
To solve this problem by using scale
factor:
1. Find the known corresponding side measurements in the first 2
triangles.
2.75 and 11
2. Divide the larger number by the smaller number.
3. Find the corresponding side to a (8) and divide it by the scale
factor of 4.
a
3
2.75
2
a = _____
8
b
11
16
24
c
b = _____
c = _____
Continue to use scale factor to find b:
1. Since the scale factor is 4 between the first 2 triangles, we can find b
by applying it to the corresponding side of b. 3
2. Multiply 3 by the scale factor of 4 to find b.
a
3
2.75
2
a = _____
8
b
11
16
24
c
12
b = _____
c = _____
Continue to use scale factor to find c:
1. Find the known corresponding side measurements in the second and
third triangles. 8 and 16
2. Divide the larger number by the smaller number.
3. Find the corresponding side to c (11) and multiply it by the scale
factor of 2.
a
3
2.75
2
a = _____
8
b
11
16
24
c
12
b = _____
22
c = _____
To solve this problem by using
proportions:
1. Find the known corresponding side measurements in the first 2
triangles.
2.75 and 11
2. Find the corresponding side to a (8).
a
3
2.75
2
a = _____
8
b
11
16
24
c
b = _____
c = _____
Continue solving this problem by
using proportions:
3. Set up the proportion in one of these two formats:
Triangle #1KnownMeasurement
CorrespondingSideMea surement
OR

Triangle #1UnknownMeasurement CorrespondingSideMea surement
Triangle #1KnowMeasurement
Triangle #2UnknownMeasurement

CorrespondingSideMea surement CorrespondingSideMea surement
a
3
2.75
a = _____
8
b
11
16
24
c
b = _____
c = _____
Finish solving this problem by using
proportions:
2.75 11

a
8
Cross multiply to solve
for missing side
2.75  8  a 11
2.75  8  11 a
11a  22.00
a2
a
3
22.00  11a
2a
8
2.75
b
11
2
a = _____
2.75 a

11
8
16
24
c
b = _____
c = _____
Finish solving this problem by using
proportions:
8
b

16 24
8  24  16  b
192  16b
12  b
a
3
Set up Proportions to
solve for b and c, then
cross multiply to solve
for missing sides.
8
2.75
b
11
2
a = _____
8 11

16 c
8 c  16 11
8c  176
c  22
16
24
c
12
b = _____
22
c = _____
An antique shop has a large dollhouse that is a model
of a real house. Here are some of the measurements:
Height
Window
Building
Dollhouse
5 cm
80 cm
Actual house
1 m (100 cm)
16 m (1600 cm)
1. What is the height of the building? (hint: 100 cm = 1 m)
Find the SCALE FACTOR between known corresponding
sides, then apply that information to find the actual building
height.
100  5  20
20  80  1600cm  16m
An antique shop has a large dollhouse that is a model
of a real house. Here are some of the measurements:
Height
Window
Building
Dollhouse
5 cm
80 cm
Actual house
1m
16 m
2. If the area of the living-room floor in the dollhouse is ¼
of a square meter, how much carpeting will be needed to
cover the floor in the real house??
Apply SCALE FACTOR squared for area, then multiply by
the amount of carpeting needed for the doll house.
20  400  .25  100m
2
2
An antique shop has a large dollhouse that is a model
of a real house. Here are some of the measurements:
Height
Window
Building
Dollhouse
5 cm
80 cm
Actual house
1m
3. If the dollhouse has 12 windows, how many windows
does the real house have?
12
4. If it takes 25 centimeters of molding to frame the door of the
dollhouse, how much molding is needed to frame the door of the
real house?
25  20  500cm 100  5m
Complete the table below.
2
5
Rectangle Scale Short Long Perimeter Area
Factor Side Side
14
10
A
1
2
5
B
2
4
10
28
40
C
5
10
25
70
250
D
½
1
2.5
7
2.5
The area of rectangle C is how
many times larger than the area
of rectangle B?
B
2
C
6
4
2 4  8
12
6 12  72 72  8  9
Scale factor squared is the difference
between the area of 2 similar figures.
3 9
2
The perimeter of rectangle C is
how many times larger than the
perimeter of rectangle B?
B
2
C
6
4
12
2(4  2)  2(6)  12
2(6  12)  2(18)  36
36 12  3
Scale factor is the
difference between
the perimeter of 2
similar figures.
SF  3
Joan used a mirror to estimate the
height of a flagpole. What is the
height of the flagpole?
5 ft
flagpole
2 ft---|-----------------9 ft-----------------------
2 5

9 x
2 x  95
x  22.5 ft
2 x  45
Find all the triangles similar to
Triangle A. ONLY D
A
B
C
D
E
12
6
3
4
5
9
3
1
3
2
12 4

9 3
6 1

3 2
3
3
1
4
3
5
2
Any questions???
Ask any questions you may have now. That is the purpose
of a review. Today and tomorrow is for questions, not the
day of the test.
 Complete the review sheet individually. While in class, if
you have a question, please ask your teacher. While
finishing the review sheet at home, write down any
questions you may have so you can ask them tomorrow.
 Come to class tomorrow with the completed review sheet.
We will discuss each question in class, and you will have
the opportunity to ask questions.
