Four-body central configurations with adjacent equal masses

For any convex non-collinear central configuration of the planar Newtonian 4-body problem with adjacent equal masses m1=m2≠m3=m4, with equal lengths for the two diagonals, we prove it must possess a symmetry and must be an isosceles trapezoid; furthermore, which is also an isosceles trapezoid when the length between m1 and m4 equals the length between m2 and m3.