Task - 40 minutes (timed) In a well-written paragraph or paragraphs describe how dilations create similar triangles and explain ways to prove two triangles are similar. → Explain how dilations create similar triangles What is a dilation? • What is a scale factor? • What is the center of dilation? Given a preimage and an image, how can you find the scale factor and center of dilation? • How does the scale factor create proportional sides? How do dilations affect the perimeter and area of similar triangles? → Explain the three additional ways to prove two triangles are similar: • What is AA-, SAS-, and SSS-? • What do dilations preserve? D. Cord

Dilations produce identical triangles when the proportional sides are generated by multiplying the scale factor while leaving the measure of the angle and the form the same.

A scale factor represents a comparision between a dimension on one geometric figure and a dimension on the other.

The dilation center is a fixed point in the plane around which all points are extended or contracted.

We define the central point of dilation and calculate the distance from this center point to a point on the preimage and also the distance from the center point to a point on the image to find the scale factor for a dilation. The Scale Factor gives us the ratio of these lengths.

The ratio which defines the proportional relationship between the sides of similar figures is the scale factor. They ought to use the same scale factor for the pairs of sides to be equal to each other.

The dilations affect the perimeter in the way that perimeter changes linearly, in direct proportion to volume, as shapes are dilated (when they become larger or smaller), while area changes quadratically, in proportion to length squared.