Infographic Geometry Problem 926: Two Equilateral Triangles, Midpoint, Perpendicular, Metric Relations. Level: High School, College, Mathematics Education

The figure below shows equilateral triangles ABC and DEF, so that M is the midpoint of AC and DE, respectively. Prove that (1) AD is perpendicular to BF, (2) . This entry contributed by Ajit Athle.