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Show that X,Y, Z are the midpoints of sides of ABC [2023 Abel, 1a]

Source:

March 12, 2024
geometry

Problem Statement

In the triangle ABCABC, XX lies on the side BCBC, YY on the side CACA, and ZZ on the side ABAB with YX∥AB,ZY∥BCYX \| AB, ZY \| BC, and XZ∥CAXZ \| CA. Show that X,YX,Y, and ZZ are the midpoints of the respective sides of ABCABC.
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