c.)+Process

= Process **Part One - The Photographs and Images** =

You will take photographs or find images on the Web of the following specific geometric relationships: ** Part Two - The Analysis ** Choose **three** out of the ten relationships above and provide some mathematical analysis to further enhance your conclusions. You may do your measurements by hand using a ruler or protractor. Think of the analysis as a way to verify the mathematical relationship. For example, if you choose to analyze relationship 6 (Similar Triangles), you may measure corresponding sides of the triangles to verify their proportionality. Or you can determine the scale factor and prove that taking a side of the smaller triangle and multiplying it by that number will yield the corresponding side of the larger triangle. The analysis section involves taking actual measurements and verifying the mathematics behind the visual representations. **Part Three - The Presentation**
 * 1) Find an example of **two parallel lines being cut by a transversal**, not at right angles, which show that the alternate interior (corresponding, alternate exterior, etc.) angles are congruent.
 * 2) Find two (or more) **congruent triangles** which show that their corresponding parts are also congruent.
 * 3) Find a **triangle inscribed in a circle** which shows that the center of the circle is also the circumcenter of the triangle.
 * 4) Find a **regular polygon with more than 4 sides**; find the measure of one interior angle and the sum of all interior angles.
 * 5) Find a (non-square) **rectangle**, and (non-square) **rhombus** and a **square** either in the same picture or separate pictures that shows the relationship between all three polygons.
 * 6) Find two **similar triangles** which demonstrate the idea of proportionality or scale factor.
 * 7) Find a **circle and its tangent** which show the properties at the point of tangency.
 * 8) Find two **non-congruent polygons** whose areas are equal.
 * 9) Find a **cylinder and a cone** that display the relationship between their volumes.
 * 10) ** Your Choice ** – may be any geometric relationship you find intriguing, interesting or perhaps puzzling. Explain why you chose this picture or image and its geometric significance.

Resoures
 * 1) Make a title slide and choose an aesthetic slide template.
 * 2) You will need one example of each of the above geometric relationships (10 photographs or images).
 * 3) Each photograph or image will be labeled (location and date) and inserted into an MS PowerPoint slide.
 * 4) On the same slide, add the relevant geometric information about the picture. For example, if you are writing about scenario #1 (parallel lines cut by a transversal), you may want to include which conjecture or definition allows you to conclude that the corresponding angles are congruent. You can add information about other angle relationships that are seen in the picture as well or what may happen to those angles if the lines were not parallel. Add about 4 bullet points of information for each picture.
 * 5) The three mathematical analysis slides should each be on a separate slide and should come after the 10 pictures.
 * 6) Write a summary slide at the end (see Conclusion below).



Use the following resources to help you focus your photographs or images so that they target a specific geometric relationship:
 * 1) The Math Forum @ Drexel, K-12 Geometry, []
 * 2) Math.com, The World of Math Online, []
 * 3) The Geometry Junkyard, []
 * 4) Home School Math, Online math quizzes, and interactive tutorials, []
 * 5) Welcome to Zona Land, The Geometry Section, []
 * 6) Geometry Online, Cynthia Lanius, []
 * 7) Geometry in Action, Architecture, []
 * 8) Congruent Figures and Triangles, []
 * 9) Math-kitecture, Student Gallery, []
 * 10) Conjectures in Geometry, []

a.) Introduction

b.) Task

d.) Evaluation

e.) Conclusion

f.) Credits