Draw triangle ABC with right angle B. How to divide this triangle into 4 equal parts?

Let’s add triangle ABC to rectangle ABCD and draw diagonals in it. At the point of intersection L, the diagonals are halved: AL = CL = BL = DL.

From point L draw perpendiculars to sides AB and BC. The LK segment will be the height and median for the isosceles triangle ALB and will divide the AB side into 2 equal parts. AK = ВK; similarly for triangle BLC: BM = CM.

Triangles AKL, BKL, BML, LMC are equal on the 3rd sign of equality of triangles (on 3 sides).