<Solid-2025-258>, hint
Since MN is perpendicular to AB, CD,
Triangle NBA , MDC are isosceles , and so NA=NB, MC=MD.
Triangles CBD , CAD are congruent
( CN=ND, BN=AN, BNㅗCD, ANㅗCD, Plane ABN ㅗ CD). Hence BC=BD=AC=AD.
Since PQ is perpendicular to AC, BD, Similarly
AB=AD=CB=CD. Hence All edges of tetrahedron ABCD are equal
sice
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