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square or not necessarily a square

Source: 45th International Tournament of Towns, Junior O-Level P2, Fall 2023

December 16, 2023

geometry

Problem Statement

2. The quadrilateral

A B C D

is convex. Its sides

A B

and

C D

are parallel. It is known that the angles

D A C

and

A B D

are equal. Furthermore the angles

C A B

and

D B C

are equal. Is

A B C D

necessarily a square? Alexandr Terteryan