# Similarity of polygons - Examples, Exercises and Solutions

The similarity between geometric figures is met when they have angles of the same size respectively and there is also proportionality between the sides of such figures.

In an intuitive way, just as it happens with triangles, two similar figures are, in fact, an enlargement of the other.

## Practice Similarity of polygons

### Exercise #1

Is rectangle ABCD similar to rectangle EFGH?

### Step-by-Step Solution

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

### Exercise #2

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

### Step-by-Step Solution

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

### Exercise #3

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?

### Step-by-Step Solution

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

### Exercise #4

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

### Video Solution

Angle C = Angle O

### Exercise #5

Which shapes are similar?

### Video Solution

The rectangles are similar.

### Exercise #1

Which figure shows a pair of similar polygons?

### Exercise #2

Which statement is true?

### Video Solution

It cannot be determined.

### Exercise #3

The polygons below are similar.

Calculate X.

2

### Exercise #4

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

4.8

### Exercise #5

Two similar rectangles are shown below.

What is the height of rectangle number 1?

1.5

### Exercise #1

Calculate X given that the polygons shown below are similar.

2

### Exercise #2

ABCD is similar to EFGH.

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

36 m

### Exercise #3

The two polygons below are similar.

Calculate the missing sides of the polygon ABCD.