$證明:因?yàn)樗倪呅?ABCD?是矩形$
$所以?AB//CD?且?AB=CD,??∠B=∠D=90°?$
$所以?∠E=∠F?$
$因?yàn)?AE=\frac {1}{2}AB,??CF=\frac {1}{2}CD,??AB=CD?$
$所以?AE=CF?$
$所以?BE= DF?$
$在?△BEH?和?△DFG ?中$
$?\begin{cases}{∠E=∠F }\\{BE=DF}\\{∠B=∠D} \end{cases}?$
$所以?△BEH≌△DFG(\mathrm {ASA})?$
$所以?DG=BH?$