geometry proof

Question

Let A,B,C,D be four distinct points such that A,B,C are noncollinear and such that the midpoint of the segment AB is the same as the midpoint of the segment CD. Prove that BC is congruent to A

Answer 1

Line segments AB and CD intersect each other in the midpoint, let's call it M.

AM=MB(definition of a midpoint)

DM=MC(def. of a midpoint)

angle AMD =angle BMC(as vertical)

triangle AMD=triangle BMC (SAS test)

BC=AD(as correspondin sides of congruent triangles