Arthur D. answered 10/07/17
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draw AD and BC so that the line segments intersect at X
connect points A and B and connect points D and C
AX≅XD definition of midpoint
BX≅XC definition of midpoint
<AXB and <CXD are vertical angles two intersecting lines form vertical angles
<AXB≅<CXD vertical angles are congruent
triangle AXB ≅ triangle DXC SAS (side-angle-side)
AB≅DC corresponding parts of congruent triangles are congruent