四邊形ABCD假設(shè)AB平行CDAC=BD角A=90度求證ABCD為平行四邊形證明：因?yàn)锳B平行CD所以角A+角C=180因?yàn)榻茿=90所以角C等于90假設(shè)角D不等于90度作BE垂直于CD,E在CD上則四邊形ABCE為矩形所以AC=BE因?yàn)锳C=BD所以BD=B...?÷?????????????????????????????????ε??????ò???????????÷?????????????????????????????????????????D???90???????????浽BD=BE??????????????????????DE??=BD??-BE??=0????DE=0????D????E???????????????ABCD????Σ??????????????????????????????D??E??????????????????????????????????????????????????????????????????????D??E?????????????????BED???????????????????????е?????ì??????????????????????????????????????????????????ü??Σ???????????????????????ɡ?????????C??0,0??A??0??a?? D??d??0?????AB???CD????AB???x??????B?????????ú?A???????B??b??a????????AC?????????a^2????BD?????????(b-d)^2+a^2???AC=BD????a^2=(b-d)^2+a^2????(b-d)^2=0b=d??B??D????????????BD?????y????AC?????BD?????????ABCD??????????????????????????????????????????????У?????????????BED????????????ù???????????????????????У???????????????????????????????????????????????????????????????????BD?????????(b-d)^2+a^2????????????b=d?????????????