<Solid-2023-239>, hint

Let P,Q,R,S be the midpoints of AB, CD, BC, AD of tetrahedron ABCD,respectively.

Since PR//SQ//= 0.5 AC and PS//RQ//=0.5BD, PRQS is rectangle and since PQ=RS

PRSQ must be a square, which means AC=BD and AC and BD are perpendicular.

Similarly AB=CD, BC=AD. Hence ABCD is a regular tetrahedron.