MathDB
|\angle BCA| + |\angle ABD| = |\angle BDA| + |\angle ACD| => KL//AC

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 2013 p5

February 15, 2020
anglesparallelogramparallelgeometry

Problem Statement

Given the parallelogram ABCDABCD such that the feet K,LK, L of the perpendiculars from point DD on the sides AB,BCAB, BC respectively are internal points. Prove that KLACKL \parallel AC when BCA+ABD=BDA+ACD|\angle BCA| + |\angle ABD| = |\angle BDA| + |\angle ACD|.