"Where there is matter, there is geometry."
- Johannes Kepler

GeometryPenrose Triangle

Introduction

This page contains resources that may be of interest to students studying Geometry. The number of resources on this page will grow as additional items are developed. If you have any questions or special requests, please contact Earl at .

Handbooks

Students of Geometry may find the following Handbooks useful as references.

PC Apps

There is no specific Geometry App, but when the student begins to study basic Trigonometry, the Trigonometry App may be of interest.

Euler Line Challenge

Here's a very cool problem that has been around for a very long time. Prove that the Centroid (intersection of medians), Orthocenter (intersection of altitudes) and Circumcenter (intersection of perpendicular bisectors) of any triangle lie on the same line. (Note: this line is called the Euler Line.)

Try to prove this yourself. One solution is provided below.

Sample Problems

The value of reviewing these sample problems and solutions is twofold. The more obvious benefit relates to problems that a student has difficulty solving themselves; a solution is provided. Less obvious is the set of techniques used in our solutions; some of the techniques used on the sample problems may not be taught in the classroom. We concentrate on efficient solutions and shortcuts; so a review of the solved problems may present new techniques that enable a student to be more efficient in their approach to solving problems.