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Level: Mathematics Education, High School, Honors Geometry, College.
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Friday, November 8, 2019
Dynamic Geometry Problem 1445: Van Aubel's theorem, Quadrilateral and Four Squares, Centers
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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