Vector geometry · demo + explainer

Midpoints join to form a parallelogram

Drag any quadrilateral ABCD. The midpoints P,Q,R,S always form a parallelogram — Varignon’s theorem. Step the vector proof.

ABCD PQ QR RS SP

Drag A, B, C, D · midpoints update live · scroll zoom · drag to pan

Show origin O
faint position vectors OA, OB, OC, OD

Opposite sides of PQRS

PQ = RS and SP = QR → parallelogram

Vector proof