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MMO 189 Moscow MO 1951 ABCD,A'B'C'D' with equal sides, unequal angles

Source:

August 7, 2019
anglesequal segmentsconvexinequalities

Problem Statement

Let ABCDABCD and A′B′C′D′A'B'C'D' be two convex quadrilaterals whose corresponding sides are equal, i.e., AB=A′B′,BC=B′C′AB = A'B', BC = B'C', etc. Prove that if ∠A>∠A′\angle A > \angle A', then ∠B<∠B′,∠C>∠C′,∠D<∠D′\angle B < \angle B', \angle C > \angle C', \angle D < \angle D'.
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