Bottema's Theorem: Triangle and Squares. Interactive Geometry Software. Level: High School, SAT Prep, College

Click the
red button ()
on the figure below to start the animation. Drag points A, C, and line
AC to change the figure. Press P and click the left mouse button to start the step by step
construction, help.

Proposition
Draw squares ABDE and BCFG on sides AB and BC of a triangle ABC. Then the midpoint M of EF is independent of B and the triangle AMC is an isosceles right triangle.

Oene Bottema (1901-1992), the great Dutch geometer, was also a good historian
of mathematics. He published several math-history articles, mainly in the
Dutch periodical "Euclides".
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Dynamic Geometry: You can alter the figure
dynamically in order to test and prove (or disproved)
conjectures and gain mathematical insight that is less
readily available with static drawings by hand.

This page uses the
TracenPoche
dynamic geometry software and requires
Adobe Flash player 7 or higher.
TracenPoche is a project of Sesamath, an association of French
teachers of mathematics.

Instruction to explore the
dynamic figure:

Animation. Click the red
button
to start/stop animation

Manipulate. Drag points A
and C, and line AC to change the figure.

Step-by-Step construction.
Press P and click the left mouse
button
on any free area of the figure
above to show the
step-by-step bar and click 'Next
Step' button ()
to start the construction step-by-step:

Hide the step-by-step bar by
using again the combination P +
click left mouse.