generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation;
Standard:
8.3.B
Description:
compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane; and
Standard:
8.3.C
Description:
use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation.
Standard:
MA.8.GR.2.2
Description:
Given a preimage and image generated by a single dilation, identify the scale factor that describes the relationship.
Standard:
MA.8.GR.2.4
Description:
Solve mathematical and real-world problems involving proportional relationships between similar triangles.
Standard:
8.10.D
Description:
model the effect on linear and area measurements of dilated two-dimensional shapes.
A dilation is a transformation in which a figure's size changes. The image which results from a dilation is similar to the original image. Corresponding sides of similar figures are proportional.
Parallelogram EFGH is a dilation of parallelogram ABCD.
So, parallelograms ABCD and EFGH are similar.
This means that the ratios of the corresponding sides are all equal.
Example:
Use two of the ratios above to set up a proportion to find EF.