Lucy Latimer acquired a new company in a hostile takeover. This new company, Math Manipulatives, needed a new logo. Ms. Latimer's husband teaches geometry, and his class submitted a logo and the following instructions for reproducing the logo:
• Begin with a large isosceles trapezoid, and locate the midpoint of each side.
• Use these midpoints as the vertices of a new quadrilateral to be formed inside the first quadrilateral.
• Locate the midpoint of each side of the second quadrilateral, and use these midpoints as vertices to form a third quadrilateral.
• Repeat this process with each new quadrilateral until the newest quadrilateral is too small to be seen.
Suppose you were one of Ms. Latimer's employees, and she assigned you the task of investigating this design proposal. Write a report to be sent to Ms. Latimer. In your report, you should include:
1. A reproduction of this design on a piece of graph paper. (You must show at least six quadrilaterals, including the first.)
2. How you know that your first quadrilateral is an isosceles trapezoid.
3. The best name (trapezoid, parallelogram, rectangle, rhombus, or square)for each subsequent quadrilateral and a convincing argument that supports the name you chose (use pg288 for reference).
4. A description of any patterns that you may find in the sequence of the shapes.
5. Definitions, postulates, and theorems from geometry to support your claims.