8.3.A 8.3.B 8.3.C MA.8.GR.2.2 MA.8.GR.2.4 8.10.D

Texas Essential Knowledge and Skills (TEKS) Dilations
Grade:	8th Grade
Standard:	8.3.A
Description:	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.

\frac{AB}{EF} = \frac{BC}{FG} = \frac{CD}{GH} = \frac{DA}{HE}

\begin{array}{rcl} \frac{AB}{EF} & = & \frac{BC}{FG} \\ \frac{5.1 cm}{EF} & = & \frac{3.6 cm}{1.8 cm} \\ (5.1 cm)(1.8 cm) & = & (EF)(3.6 cm) \\ \frac{(5.1 cm)(1.8 cm)}{(3.6 cm)} & = & EF \\ 2.55 cm & = & EF \end{array}

Texas Essential Knowledge and Skills (TEKS)

Dilations

8.3.A

generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation;

8.3.B

compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane; and

8.3.C

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.

MA.8.GR.2.2

Given a preimage and image generated by a single dilation, identify the scale factor that describes the relationship.

MA.8.GR.2.4

Solve mathematical and real-world problems involving proportional relationships between similar triangles.

8.10.D

model the effect on linear and area measurements of dilated two-dimensional shapes.

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