ProvingTrianglesSimilar

A dilation stretches or shrinks a figure by a determined scale factor

If the Scale Factor (SF) is greater than 1, it is a stretch, or enlargement.

If the Scale Factor (SF) is less than 1, it is a shrink, or reduction.

If the Scale Factor (SF) is equal to 1, there is no change, and the figures will also be congruent.

On the coordinate plane, a preimage is dilated about a point, which can be the origin

The point is called the center of dilation

1. Draw a line from the center of dilation to a point on the preimage

Measure the length and multiply that length by the Scale Factor.

Draw a line from the center of dilation through the original point with the dilated length.

Mark that point as A¹ (A prime)

Repeat the process for all of the points in the preimage, denoting the points of the dilated image with "tick" marks to indicate "prime"

Connect the points to form the new image.

The new figure should have the shape, but not the same size

composition (multiple transformations on the same object) of one or more rigid motions (translation, reflection, rotation) and a dilation

Result in an image that is similar to the original figure (preimage)

Symbol for similar is  $\sim$  

All rigid motions are also similarity transformations

All dilations are similarity transformations

All compositions of a dilation and a rigid motion are similarity transformations

Written as DkRxor y-axis or DkT(transformation rule) or Dkr(number of degrees)

Produce similar figures

Corresponding angles of the similar figures are the same (the sum of the angles of a triangle = 180^o for all triangles)

The corresponding sides of a preimage and the resulting image are proportional. The proportion is the Scale Factor