Geometry · Midline theorem · Quadrilaterals · Equilateral triangle
Problem 2, 2016
In a quadrilateral \(ABCD\) the sides \(AD\) and \(BC\) are equal, and the interior angles at \(A\) and \(B\) satisfy
\[ \angle DAB + \angle ABC = 120^\circ . \]
Prove that the midpoint of the diagonal \(AC\), the midpoint of the diagonal \(BD\) and the midpoint of the side \(CD\) are the vertices of an equilateral triangle.
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Serbian Regional Competition (Okruzno takmicenje) 2016, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source