3.1.5 Using Transformations to Create Polygons HW: 3-55,56,57,60 October 11, 2018

Objectives CO: SWBAT use transformations to make other polygons. LO: SWBAT discuss with their teammates how they can rotate and reflect to create other polygons.

Participation Quiz 3-51. THE SHAPE FACTORY The Shape Factory, an innovative new company, has decided to branch out to include new shapes.  As product developers, your team is responsible for finding exciting new shapes to offer your customers.  The current company catalog is shown at right. Since your boss is concerned about production costs, you want to avoid buying new machines and instead want to reprogram your current machines.  The factory machines cannot only make all the shapes shown in the catalog, but are also able to rotate or reflect a shape exactly one time.  For example, if the half-equilateral triangle is rotated 180° about the midpoint (the point in the middle) of its longest side, as shown at right, the result is a rectangle. Your Task: Your boss has given your team until the end of this lesson to find as many new shapes as you can.  Your team’s reputation, which has suffered recently from a series of blunders, could really benefit from an impressive new line of shapes formed by a triangle and its transformations.  For each triangle in the catalog, determine which new shapes are created when it is rotated or reflected exactly one time so that the image shares an entire side with the original triangle.  Be sure to make as many new shapes as possible.  Use tracing paper or any other reflection tool to help. Participation Quiz

Reflections Rotations

3-54. BUILDING A CATALOG What other shapes can be created through reflection and rotation?  Explore this as you answer the questions below.  You can investigate these questions in any order.  Remember that the resulting shape includes the original shape and all of its images.  Remember to record and name each result. What if you reflect an equilateral triangle twice, once across one side and another time across a different side? Isosceles Trapezoid What if an equilateral triangle is repeatedly rotated about one vertex so that each resulting triangle shares one side with another until new triangles are no longer possible?  Describe the resulting shape. Regular Hexagon What if you rotate a trapezoid 180º around the midpoint of one of its non-parallel sides? Parallelogram