It is a parallelgram that is cut in half by a diagnoal line making two triangles

Gray,

Here is another approach. After drawing the parallelogram try to prove that the two triangles formed by drawing the diagonal are congruent. Since we have a parallelogram we already know that AB=CD and that BC=DA. Since the diagonal BD is the same line for both triangles then we can prove congruency by SIDE SIDE SIDE. Congruent triangles have equal perimeters.