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Online Math: Geometry Problem 1219: Equilateral Triangles, Midpoints, 60 Degrees, Congruence, Rhombus. Tiled background image: Intihuatana, Machu Picchu. Level: College, High School.

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In the figure below, equilateral triangles ABC1 and A1BC are drawn on the sides of a triangle ABC. If B1, B2, B3, and B4 are the midpoints of AC, AC1, A1C, and A1C1, respectively, prove that (1) triangles B1B2B4 and B1B3B4 are equilateral; (2) B1B2B4B3 is a rhombus; (3) angle B2B1B3 = angle B2B4B3 = 120 degrees; (4) B2B3 and B1B4 are perpendicular.
 
 

Geometry Problem 1219: Scalene Triangle, Equilateral Triangles, Midpoints, 60 Degrees, Congruence, Rhombus.
 
 

 

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Last updated: May 29, 2016