Examples with solutions for Similarity of Polygons: Identifying and defining elements

Exercise #1

1027.51.5The two parallelograms above are similar. The ratio between their sides is 3:4.

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

Video Solution

Step-by-Step Solution

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

32:42=9:16 3^2:4^2=9:16

Answer

9:16

Exercise #2

Is rectangle ABCD similar to rectangle EFGH?

777333101010666AAABBBDDDCCCEEEFFFHHHGGG

Video Solution

Step-by-Step Solution

We first need to verify the ratio of similarity.

We examine if:

ABEF=ACEG \frac{AB}{EF}=\frac{AC}{EG}

To do this, we substitute our values in:

710=36 \frac{7}{10}=\frac{3}{6}

71012 \frac{7}{10}\ne\frac{1}{2}

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

Answer

No

Exercise #3

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

4.54.54.50.750.750.753334443336663330.50.50.52222.662.662.66222444AAABBBCCCDDDEEEFFFMMMNNNOOOPPPRRRJJJ

Video Solution

Answer

Angle C = Angle O

Exercise #4

Which shapes are similar?

8888881212126668886661414146661414143.53.53.51.51.51.53.53.53.561.5

Video Solution

Answer

The rectangles are similar.

Exercise #5

Which figure shows a pair of similar polygons?

Video Solution

Answer

333333333333555555555555

Exercise #6

Which statement is true?

Video Solution

Answer

It cannot be determined.