## Summary Lesson on Euler's Line and Menelaus' Theorem

3oct10

\begin{document} \maketitle \section{Introduction} We reviewed the lab experiment constructing the Euler line according to Court's proof that the altitudes of a triangle are concurrent. A brief review of the Lesson A8 (in the notes) that Menelaus' Theorem implies Ceva's Theorem is illustrated by a screen shot from the class. \section{Court's Proof and the Euler Line} See Section 2 of the original lesson on dilatations online at MA403 portal page > Class Webpages > Dilatations. In this edition of the course we shall not cover the remainder of this lesson, and substitute an abbreviated version on W6 with an active learning session on F6 on the same subject. \section{Menelaus implies Ceva} This very short lesson at MA403 portal page > Class Webpages > Affine > A8 is left to the student. You should work through the proof and write it up in your journal. This is a typical question on the final for this course. In the picture, the point is that inside the figure for Ceva, there are three similar Menelaus figures. The screen shot shows one of them. The labelling is intentionally left off, and you should supply the labels correctly. \end{document}