设AC和BD相交于点O,连接OE.
OE是Rt△ACE斜边上的中线,可得:AC = 2OE ;
OE是Rt△BDE斜边上的中线,可得:BD = 2OE ;
所以,AC = BD .
因为,ABCD是平行四边形,AC = BD ,
所以,ABCD是矩形.
如图,已知在平行四边形ABCD中,以AC为斜边作Rt△AEC,∠BED=90°.求证平行四边形ABCD是矩形.
如图,已知在平行四边形ABCD中,以AC为斜边作Rt△AEC,∠BED=90°.求证平行四边形ABCD是矩形.
数学人气:476 ℃时间:2019-12-20 09:55:50
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