<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