Given:[br][math]\overline{AB}\cong\overline{CD}[/math][br][math]\overline{BC}\cong\overline{AD}[/math][br][math]M[/math] is the midpoint of [math]\overline{AC}[/math][br][math]N[/math] is the midpoint of [math]\overline{BD}[/math][br][br]Prove:[br][math]\overleftrightarrow{MN}[/math] is the perpendicular bisector of [math]\overline{AC}[/math] and [math]\overline{BD}[/math][br]

You can click and drag on the diagram to rotate it.[br][br]You may also click and drag points [math]A[/math], [math]B[/math], and [math]C[/math] in the plane to change the shape of the figure. The given information will be preserved. Point [math]D[/math] can also be dragged to a new position, but none of these changes will affect the given information or the conclusion.