Prove equivalence of particular areas in generic quadrilateral

Question

I am a university student taking a course in Mathematics Teaching, and one assignment is the following problem, to be solved using only Euclidean geometry as is presented in Euclid's Elements. Unfortunately I have no idea where to start.

While I am required to present a very formalized solution, as if it were a proposition in Euclid's book, I am confident in my ability to produce it if I had just an idea for a solution to this problem.

Here is the problem:

Consider a quadrilateral $ABCD$, and $M_1 ... M_4$ the midpoints of its sides $AB, ..., DA$ respectively. Draw the segments $AM_3, BM_4, ...$ as in the picture. Show that the triangles $t_1, ...., t_4$ have total area equal to that of the quadrilateral $q_1$

Thank you.