Geometry, Theorems and Problems

Geometry Problem 1230: Quadrilateral, 60 Degrees, Congruence, Metric Relations, Area. Tiled background image: Intihuatana, Machu Picchu. Level: College, High School.

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In a quadrilateral ABCD, angle A = angle D = 60 degrees, AC = BD, AB = a, AD = 3a, and the length of CD is greater than the length of AB. AC and BD intersect at E. Prove that (1)Formula to prove; (2) AE = 3BE; (3) BC is perpendicular to CD; (4) Formula to prove 3; (5) Formula to prove area. (Trigonometry is not allowed.)
This entry contributed by Sumith Peiris, Moratuwa, Sri Lanka. 
 

Geometry Problem 1230: Quadrilateral, 60 Degrees, Congruence, Metric Relations.
  

 

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Last updated: Jul 6, 2016