Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

## Friday, November 8, 2019

### Dynamic Geometry Problem 1445: Van Aubel's theorem, Quadrilateral and Four Squares, Centers

Labels:
dynamic geometry,
GeoGebra,
Problem,
quadrilateral,
square,
theorem,
van Aubel

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https://photos.app.goo.gl/ev2e1gUgH5YBtTrP7

ReplyDeleteLet S is the midpoint of BD

Consider triangle ABD and squares ADKL and ABFE

Per the result of problem 497 we have SM=SN and SM⊥SN

Consider triangle BCD and squares DCIJ and BCHG

We also have SP=SO and SP⊥SO

Triangle SOM is congruent to SPN ( case SAS)

And triangle SOM is the image of SPN in the rotational transformation, center S

And angle of rotation= 90

So MO=PN and MO⊥PN