In Module 2, Topic A students revisit what scale drawings are and discover two systematic methods of how to create them using dilations. The comparison of the two methods yields the Triangle Side Splitter Theorem and the Dilation Theorem.

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**Standard(s): **
[MA2015] GEO (9-12) 12 :

[MA2019] GEO-19 (9-12) 36 :

12 ) Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. *Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.* [G-CO12]

[MA2019] GEO-19 (9-12) 36 :

36. Use geometric shapes, their measures, and their properties to model objects and use those models to solve problems.

[MA2019] GEO-19 (9-12) 38 : 38. Use the mathematical modeling cycle involving geometric methods to solve design problems.

*Examples: Design an object or structure to satisfy physical constraints or minimize cost; work with typographic grid systems based on ratios; apply concepts of density based on area and volume.*

Discover parallels between the natural world and origami—the Japanese art of paper folding—and witness how artists, mathematicians, and scientists are pioneering complex new designs, in this video from *NOVA: The Origami Revolution*. While origami is steeped in tradition, computer programs are being used today to develop new, more complex designs so that almost any three-dimensional object can be translated into a two-dimensional pattern that can be folded to model the object. This resource is part of the NOVA Collection.

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**Standard(s): **
[MA2015] GEO (9-12) 17 :

[MA2019] GEO-19 (9-12) 26 :

17 ) Prove theorems about triangles. *Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity.* [G-SRT4]

[MA2019] GEO-19 (9-12) 26 :

26. Verify experimentally the properties of dilations given by a center and a scale factor.

a. Verify that a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

b. Verify that the dilation of a line segment is longer or shorter in the ratio given by the scale factor.

[MA2019] GEO-19 (9-12) 38 : 38. Use the mathematical modeling cycle involving geometric methods to solve design problems.

*Examples: Design an object or structure to satisfy physical constraints or minimize cost; work with typographic grid systems based on ratios; apply concepts of density based on area and volume.*