Two figures are said to be similar if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal.
This common ratio is called the scale factor .
The symbol is used to indicate similarity.
In the figure below, pentagon pentagon .
(Note that the order in which you write the vertices matters; for instance, pentagon is not similar to pentagon .)
The two cylinders are similar. Find the scale factor and the radius of the second cylinder.
The height of the cylinder on the right is the height of the cylinder on the left. So, the scale factor is .
To get the radius of the smaller cylinder, divide by .
So, the radius of the smaller cylinder is cm.
In the figure above, the hexagon is flipped horizontally to get .
Then hexagon is translated to get .
Hexagon is dilated by a scale factor of to get .
That is, all four hexagons are similar. (In fact, the first three are congruent.)
Consider pentagon on a coordinate plane.
A rotation by about the origin takes the pentagon to .
Now, a dilation about the origin by a scale factor takes the pentagon to .
Note that . That is, all three pentagons are similar. (And the first two are congruent.)