Question 27
In the trapeze $ABCD$ the sides $AB$ and $CD$ are parallel, the angles $\widehat{ABC}$ and $\widehat{BAD}$ are acute. Prove that it is possible to divide the triangle $ABC$ into 4 disjoint triangles $X_{1}, \ldots, X_{4}$ and the triangle $ABD$ into 4 disjoint triangles $Y_{1}, \ldots, Y_{4}$ such that the triangles $X_{i}$ and $Y_{i}$ are congruent for each $i$.