This page is a record of labs, with links to some lab sheets and other lab materials for Math 487.
Lab 1. September 27.
Introduction to Sketchpad based on notes: Getting Acquainted with Sketchpad. Major constructions are equilateral triangle and midpoint triangle.
Further introduction to Sketchpad (traces and buttons and scripts). Geometry topics center on concept of equal distance, perpendicular bisectors and families of circles. Line reflection is introduced.
The Carpenter's Principle is the topic of this lab. First are experments discovering apparent facts about a locus or right angles and also about subtriangles of right triangles. Then students are given beginning sketches that parallel approaches to proof that in a right triangle, the midpoint of the hypotenuse is equidistanct from all three vertices.
The midpoint divides a segment into two congruent pieces, but the midpoint can also be viewed as an instance of similarity, scaling by the ratio one-half. Seeing this leads to theorems such as the Midpoint Quadrilateral Theorem. Another point of view is that the midpoint of a segment is the center of a point reflection that exchanges endpoints of the segment. This viewpoint leads to ways of building a quadrilateral from its midpoint parallelogram.
Lab 5. October 25. Part 1 and Part 2-3 are separate web pages. Also in PDF format (Part 1 in PDF or Part 2 in PDF), which show graphics more clearly.
This lab mixes hands-on and Sketchpad. In Part 1, the hands-on approach to inscribed angles is based on cutting out angles from paper. In part 2, the study of inscribed angles is continued with Sketchpad. Part 3 is a return to the themes of Lab 04, with a sketch of a figure with medians and midpoints.
Lab 6. November 1. Review for Midterm.
Lab 7. November 8. Introduction to Transformations.
Lab 8. November 15. Composing Transformations.
Lab 9. November 22. Symmetry.
Lab 10. November 29. Dilations.
Lab 11. December 6. Dissections.