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.
Monday, March 9, 2020
Dynamic Geometry 1460: Newton-Gauss Line, Complete Quadrilateral, Midpoints of Diagonals
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https://photos.app.goo.gl/fuXMGA8D5W6nwNzV8
ReplyDeleteDefine points K, P, Q as midpoint of CF, DF, CD ( see sketch)
Note that T, K, P are collinear
Same as W,Q,P and N, Q, K
Consider triangle CDF and secant ABF, we have
EC/ED x BC/BF x AD/AF = 1…..(1)
But EC/ED= TK/TP ; BC/BF= WP/WQ ; AD/AF=NQ/NK
Replace it in ( 1) then we have TK/TP x WP/WQ x NQ/NK= 1
So N, W, T are colinear per Menelaus’s theorem