Nonconcurrent triangles with parallel sides are always homothetic. Homothetic triangles are always perspective triangles. Their perspector is called their homothetic center.
Homothetic Triangles
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Cite this as:
Weisstein, Eric W. "Homothetic Triangles." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HomotheticTriangles.html