6.7.1 Perform Similarity Transformations

Remember previous we talked about 3 types of CONGRUENCE transformations, in other words, the transformations performed created congruent figures Rotation, Reflection, and translation

We also discussed Dilations but not in great detail, now we will

A Dilation is a SIMILARITY transformation, in that by using a scale factor, the transformed object is similar to the original with congruent angles and proportional side lengths.

REDUCTION VS ENLARGEMENT For k, a scale factor we write (x, y) (kx, ky) For 0 < k < 1 the dilation is a reduction For k > 1 the dilation is an enlargement

Let ABCD have A(2, 1), B(4, 1), C(4, -1), D(1, -1) Scale factor: 2

Use the distance formula and SSS to verify they are similar

Usually the origin (if not re-orient) To show two objects are similar, we

draw a line from the origin to the object further away, if the line passes through the closer object in the similar vertex then the objects are similar.

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