Superlesson
Project 6-1

Superlesson
Project 6-2

Superlesson
Project 6-3

Geometry

Chapter 6, Polygons and Polyhedrons

Quadrilaterals are used in various types of artwork quite frequently. In this activity, you will see how quadrilaterals are used in decorative glass designs and how knowledge of the properties of various quadrilaterals can help artists create the desired shapes.

Part B, Proving Quadrilaterals Are Parallelograms

1. Look at stained glass designs by Frank Lloyd Wright.

a. Parallelograms play a major part in many of Wright's designs. Without actually checking that both pairs of opposite sides are parallel, how could an artist be sure that a quadrilateral is truly a parallelogram using only a ruler?

b. How could the artist be sure that the quadrilaterals are truly parallelograms using only a protractor?

Part C, Proofs with Special Parallelograms

2. Look at some designs using Beveled and textured glass. The first window you see has a square frame with the diagonals creating part of a flower design. Describe the shape of the first window with the flower design. What is true about the diagonals for this shape?

3. Peer through some amazing skylights at the following Web site.

a. Now look at a Skylight. The first window on this page has a regular octagonal frame. Each of the eight radiating sections of the octagon is composed of three quadrilaterals which appear to be trapezoids. Explain how the artist would know each of these shapes was a trapezoid if he or she knew that exactly two pairs of consecutive angles were supplementary.

b. What are the measures of these pairs of supplementary angles?