Similarity and Transformations

what you need to know by Brianna Mack

How can you identify similarity?

If you can map a figure onto another figure by using a sequence of transformations and dilations, the two figures are similar.

Determine if the two triangles are similar. Refer to the image above.

Because the figures are layed out the same way, one of the translations is automatically going to be a translation.A translation is how you move a figure on its x and y axis. now when you are trying to figure out similarities, you have to write ratios of each side.

AB/DE=10/20 or one half. BC/EF=6/12 or one half. CA/FD=7/14 or one half also.

Because the ratios are equal, triangle ABC will be dilated to triangle DEF. a dilation is when you change a figures size. That means the figures are similar and can be translated and dilated to map ABC onto DEF.

Determine if the two triangles are similar. Refer to the image above.

Because the orientation of my figures are the same, one of my transformations is automattically going to be a translation.

Write the ratios

AB/DE=3/7    BC/EF=2/5.

Since my ratios are NOT equal, these triangles are not similar


Here's a real world example

For this example, refer to the image above. Tommy enlarges this photo by a scale factor of three. What are the new demensions of this photo? Is the new photo similar to the original?

First you have to multiply the original photo by 3 to find the dimensions of the enlarged photo

4in. x  3=12in.                      6in. x 3=18in.

The new dimensions would be 12in. by 18in. That means the new demensions are similar to the original.

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