MathDB
<BXD - <BYD = <BSD if <AXC - <AYC = <ASC, trapezoid ABCD

Source: 2021 Sharygin Geometry Olympiad Finals grades X-XI p6

August 2, 2021
geometrytrapezoidanglesequa angles

Problem Statement

The lateral sidelines ABAB and CDCD of trapezoid ABCDABCD meet at point SS. The bisector of angle ASCASC meets the bases of the trapezoid at points KK and LL (KK lies inside segment SLSL). Point XX is chosen on segment SKSK, and point YY is selected on the extension of SLSL beyond LL such a way that AXCAYC=ASC\angle AXC - \angle AYC = \angle ASC. Prove that BXDBYD=BSD\angle BXD - \angle BYD = \angle BSD.