MathDB

7

Part of 1993 Poland - First Round

Problems(1)

Relationships between triangles and parallelograms

Source: Poland Math Olympiad 1993 Round 1 #7

6/3/2023
Given convex quadrilateral ABCDABCD. We construct the similar triangles APB,BQC,CRD,DSAAPB, BQC, CRD, DSA outside ABCDABCD so that ∠PAB=∠QBC=∠RCD=∠SDA,∠PBA=∠QCB=∠RDC=∠SAD\angle PAB = \angle QBC = \angle RCD = \angle SDA, \angle PBA = \angle QCB = \angle RDC = \angle SAD. Prove that if PQRSPQRS is a parallelogram, so is ABCDABCD.
geometrysimilar trianglesparallelogram