<Qua-2023-714> hint

Suppose 4 triangles are folded as directed, then points A,B,C,D coincide, point T.

Since PT=PA=PB, points A,T,B lie  on a circle centered at P, 

Hence angle ATB is right. Similarly angles BTC,CTD,DTA are right,  which means 

AC and BD are perpendicular.