Similarity and Transformations

Identify Similarity

Vocabulary

Similar- if one image can be obtained from another by a sequence of transformations and dilations.

Scale factor- The ratio of the lengths of two corresponding side of two similar polygons.

Transformation- An operation that maps a geometric figure, pre-image, onto a new figure, image.

Example #1

Step 1: List the type of transformations that the figure has.  For example, the figure above is in the same orientation so the transformation is translation and dilation.

Step 2: Translate the smaller figure to the larger figure and write ratios comparing the side lengths of each side.

All ratios are equal to 1/2. So triangle ABC is similar to triangle XYZ because a translation and a dilation maps triangle ABC onto triangle XYZ.

Example #2

Step 1:  List the type of transformations that the figure has.  For example, the figure above is in the same orientation so the transformation is translation and dilation.

Step 2: Translate the smaller figure to the larger figure and write ratios comparing the side lengths of each side.

All ratios are not equal, so therefore triangle DEF is not similar to triangle ABC.

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