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equal angles wanted inside a parallelogram, parallel, angle bisectors

Source: 2005 Oral Moscow Geometry Olympiad grades 8-9 p2

October 16, 2020
geometryparallelogramequal anglesangle bisector

Problem Statement

A parallelogram of ABCDABCD is given. Line parallel to ABAB intersects the bisectors of angles AA and CC at points PP and QQ, respectively. Prove that the angles ADPADP and ABQABQ are equal.
(A. Hakobyan)