Similarity of Polygons - Examples, Exercises and Solutions

Is rectangle ABCD similar to rectangle EFGH?

We first need to verify the ratio of similarity.

We examine if:

$\frac{AB}{EF}=\frac{AC}{EG}$

To do this, we substitute our values in:

$\frac{7}{10}=\frac{3}{6}$

$\frac{7}{10}\ne\frac{1}{2}$

The ratio is not equal, therefore the rectangles are not similar.

No

Look at the two similar rectangles below and calculate the perimeter of the larger rectangle.

Let's remember that in a rectangle there are two pairs of parallel and equal sides.

We will call the small triangle 1 and the large triangle 2.

We calculate the perimeter of the small triangle:

$P_1=2\times3.5+2\times1.5=10$Since we know that the rectangles are similar:

$\frac{3.5}{14}=\frac{p_1}{p_2}$

We place the data we know for the perimeter:

$\frac{3.5}{14}=\frac{10}{p_2}$

$\frac{3.5}{14}\times p_{_2}=10$

$p_2=10\times\frac{14}{3.5}$

$P_2=40$

40 cm

The two parallelograms above are similar. The ratio between their sides is 3:4.

What is the ratio between the the areas of the parallelograms?

The square of the ratio between the sides is equal to the ratio between the areas of the parallelograms:

$3^2:4^2=9:16$

9:16

In front of you are two hexagons with a similarity ratio. Which angles are corresponding?

Angle C = Angle O

Which shapes are similar?

The rectangles are similar.

Which figure shows a pair of similar polygons?

Which statement is true?

It cannot be determined.

The polygons below are similar.

Calculate X.

2

Calculate X given that the polygons shown below are similar.

2

ABCD is similar to EFGH.

If the perimeter of ABCD is 54 m, then what is the perimeter of EFGH?

36 m

Two similar rectangles are shown below.

What is the height of rectangle number 1?

1.5

Calculate the length of AB given that the triangles below are similar.

4.8

The price of a square rug that is 2 meters long is $600.

What is the price of a square rug that has a side length of 3 meters?

$1350

Fatima receives $350 for her work on a garden that measures 10 meters by 10 meters.

How much will she receive for working on a garden measuring 20 meters by 20 meters?

$1400

Ariel paid $5,000 for the installation of a large door measuring 6 meters by 4.5 meters.

How much will Ariel pay for installing another door measuring 2 meters by 1.5 meters?

$555.5