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Geometry Problem 1344: Bottema's Theorem, Triangle, Two Squares, Midpoint


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 triangles AMC and DMG are an isosceles right triangles.

Problem 1344, Bottema theorem, triangle, squares, midpoint

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".
Background image: Rector Magnificus Oene Bottema. Source: Wikipedia, Oene Bottema 

Bottema's Theorem, Interactive Geometry Software: TracenPoche

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.


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.

Bottema's Theorem on Twitter:

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Last updated: August 1, 2009