Similarities and Transformation

Similar and Transformed Figures

The Different Types of Transformation

There are four types of transformation. The different types of transformations are reflection, rotation, dilation, and translation. Reflection is when a figure is flipped over a line. Rotation is when the figure is rotated by a fixed point. Dilation is when a figure enlarges or reduces by a scale factor. Translation is when a figure slides from one position to another position without any turning. Those are the four types of transformation. A figure can have more than one transformation.

The Steps to Identify Similar Figures

  • When a two figures are similar, it means that the second figure can be obtained from the first by a sequence of transformation and dilation .
  • First, you need to determine the transformation used on the figures
  • Then, you need to write ratios comparing the lengths of each side
  • Reduce the ratios if needed
  • If the ratios are the same, then the figures are similar, but if there are different ratios, then the figure isn't similar.

* Something that you should keep in mind is that a figure can have more than one transformation.

Example:

side AB=5 and side DE= 10, and when you reduce the ratio, you get 1/2

side BC=8 and side EF=16, when you reduce the ratio, you get 1/2

side CA=10 and side FD=20, when you reduce the ratio, you get 1/2

~ Since the ratios are all equal, triangle DEF is a dilated image to triangle ABC. So, the two triangles are similar.

The Steps to Solve Similar Figures but Different Sizes

  • You would first need to determine the transformation used
  • Then you would write ratios comparing the lengths of each side.
  • Reduce down the ratio if needed
  • If all of the ratios are the same, then the figures are equal. If the ratios are not equal, then the figures aren't equal.

Example:

The Blue rectangle

width=20 and length=45, when you reduce it down, you get the ratio of 4/9

The Yellow rectangle

width=25 and length=40, when you reduce the ratio down, you get 5/8

~ The ratios are not equal. So, since the ratios aren't equal, the rectangles aren't similar.

Dealing with Scale Factor

      Similar figures have the same shape but different sizes. The sizes of the two figures are related to the scale factor of the dilation. A scale factor is the ratio of the lengths of two corresponding sides of two similar figures.

side AT= 12 and side GD=3, the scale factor for that side is 4

side TC=8 and side DO=2, the scale factor for that side is 4

side CA=16 and side OG=4, the scale factor of that side is 4

~ The scale factor of these two triangles is 4, because when you write the ratios, you get 4 at the end.