Similarity of Geometric Figures

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.