£¨Àí¿Æ£©ÈçͼµÄ¶àÃæÌåÊǵ×ÃæΪƽÐÐËıßÐεÄÖ±ËÄÀâÖùABCD-A1B1C1D1£¬¾­Æ½ÃæAEFGËù½ØºóµÃµ½µÄͼÐΣ®ÆäÖСÏBAE=¡ÏGAD=45¡ã£¬AB=2AD=2£¬¡ÏBAD=60¡ã£®

£¨¢ñ£©ÇóÖ¤£ºBD¡ÍƽÃæADG£»
£¨¢ò£©ÇóƽÃæAEFGÓëƽÃæABCDËù³ÉÈñ¶þÃæ½ÇµÄÓàÏÒÖµ£®

£¨ÎÄ¿Æ£©Èçͼ£¬ABΪԲOµÄÖ±¾¶£¬µãE¡¢FÔÚÔ²OÉÏ£¬AB¡ÎEF£¬¾ØÐÎABCDËùÔÚµÄƽÃæºÍÔ²OËùÔÚµÄƽÃ滥Ïà´¹Ö±£¬ÇÒAB=2£¬AD=EF=1£®
£¨¢ñ£©ÇóÖ¤£ºAF¡ÍƽÃæCBF£»
£¨¢ò£©ÉèFCµÄÖеãΪM£¬ÇóÖ¤£ºOM¡ÎƽÃæDAF£®

£¨Àí¿Æ£©½â£º£¨¢ñ£©Ö¤Ã÷£ºÔÚ¡÷BADÖУ¬AB=2AD=2£¬¡ÏBAD=60¡ã£¬
ÓÉÓàÏÒ¶¨ÀíµÃ£¬BD=¡àAB2=AD2+BD2£®
¡àAD¡ÍBD
ÓÖGD¡ÍƽÃæABCD
¡àGD¡ÍBD£¬
GD¡ÉAD=D£¬
¡àBD¡ÍƽÃæADG£¬

£¨¢ò£©ÒÔDΪ×ø±êÔ­µã£¬OAΪxÖᣬOBΪyÖᣬOGΪzÖὨÁ¢¿Õ¼äÖ±½Ç×ø±êϵD-xyz
ÔòÓÐA£¨1£¬0£¬0£©£¬B£¨0£¬£¬0£©£¬G£¨0£¬0£¬1£©£¬E£¨0£¬£©
ÉèƽÃæAEFG·¨ÏòÁ¿Îª=£¨x£¬y£¬z£©
Ôò£¬
È¡£¬
ƽÃæABCDµÄÒ»¸ö·¨ÏòÁ¿£¬
ÉèÃæABFGÓëÃæABCDËù³ÉÈñ¶þÃæ½ÇΪ¦È£¬
Ôò£®

£¨ÎÄ¿Æ£©½â£º£¨¢ñ£©Ö¤Ã÷£º¡ßƽÃæABCD¡ÍƽÃæABEF£¬CB¡ÍAB£¬
ƽÃæABCD¡ÉƽÃæABEF=AB£¬¡àCB¡ÍƽÃæABEF£¬
¡ßAF?ƽÃæABEF£¬¡àAF¡ÍCB£¬
ÓÖ¡ßABΪԲOµÄÖ±¾¶£¬¡àAF¡ÍBF£¬¡àAF¡ÍƽÃæCBF£®
£¨¢ò£©ÉèDFµÄÖеãΪN£¬ÔòMN£¬ÓÖAO£¬ÔòMNAO£¬MNAOΪƽÐÐËıßÐΣ¬
¡àOM¡ÎAN£¬ÓÖAN?ƽÃæDAF£¬OM?ƽÃæDAF£¬¡àOM¡ÎƽÃæDAF£®
·ÖÎö£º£¨Àí¿Æ£©£¨I£©ÓÉÌâÔÚ¡÷BADÖУ¬Í¨¹ý¼ÆËãµÃµ½AD¡ÍBD£¬ÔÙÀûÓÃÌõ¼þÏßÃæ´¹Ö±µÃµ½ÏßÏß´¹Ö±£¬½ø¶øµÃµ½ÒªÖ¤µÄÏßÃæ´¹Ö±£»
£¨II£© ÓÉÌâÒ⼰ͼÐÎÌص㽨Á¢ÈçͼµÄ¿Õ¼äÖ±½Ç×ø±êϵ£¬ÀûÓÃƽÃæµÄ·¨ÏòÁ¿µÄ¼Ð½ÇÓë¶þÃæ½ÇµÄ´óС֮¼äµÄ¹ØϵÇó³ö¶þÃæ½ÇµÄ´óС£®
£¨ÎÄ¿Æ£©£¨I£©ÓÉÌâÒ⼰ƽÃæABCD¡ÍƽÃæABEFÇÒCB¡ÍAB£¬ÀûÓÃÃæÃæ´¹Ö±µÄÐÔÖʶ¨ÀíµÃµ½ÏßÃæ´¹Ö±£¬ÔÚÀûÓÃÔ²µÄÖ±¾¶Ëù¶ÔµÄÔ²ÖܽÇΪֱ½ÇµÄÐÔÖʵõ½ÏßÏß´¹Ö±£¬½ø¶øÀûÓÃÏßÃæ´¹Ö±µÄÅж¨¶¨ÀíµÃ³öÒªÖ¤Ã÷µÄ½áÂÛ£»
£¨II£©ÓÉÌâÒâ¼°Ìõ¼þ½èÖúÏßÏßƽÐеõ½ÏßÃæƽÐУ¬ÔÙÀûÓÃÏßÃæƽÐеÄÐÔÖʶ¨ÀíµÄµÃµ½ËùÖ¤£®
µãÆÀ£º£¨Àí¿Æ£©´ËÌâÖص㿼²éÁËÏßÃæ´¹Ö±µÄÅж¨¶¨Àí¼°ÐÔÖʶ¨ÀíµÈ֪ʶ£¬»¹¿¼²éÁËÀûÓÿռäÏòÁ¿µÄ֪ʶÇó½â¶þÃæ½ÇµÄ´óСµÄ֪ʶ£®
£¨ÎÄ¿Æ£©´ËÌâÖص㿼²éÁËÃæÂôŪ´¹Ö±µÄÅж¨¶¨Àí¼°ÏßÃæ´¹Ö±µÄÅж¨¶¨Àí£¬»¹¿¼²éÁËÏßÃæƽÐеÄÅж¨¶¨Àí¼°Æ½ÐÐÖ±Ïß¼äµÄƽÐоßÓд«µÝÐÔ£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨Àí¿Æ£©ÈçͼµÄ¶àÃæÌåÊǵ×ÃæΪƽÐÐËıßÐεÄÖ±ËÄÀâÖùABCD-A1B1C1D1£¬¾­Æ½ÃæAEFGËù½ØºóµÃµ½µÄͼÐΣ®ÆäÖСÏBAE=¡ÏGAD=45¡ã£¬AB=2AD=2£¬¡ÏBAD=60¡ã£®
¾«Ó¢¼Ò½ÌÍø
£¨¢ñ£©ÇóÖ¤£ºBD¡ÍƽÃæADG£»
£¨¢ò£©ÇóƽÃæAEFGÓëƽÃæABCDËù³ÉÈñ¶þÃæ½ÇµÄÓàÏÒÖµ£®

£¨ÎÄ¿Æ£©Èçͼ£¬ABΪԲOµÄÖ±¾¶£¬µãE¡¢FÔÚÔ²OÉÏ£¬AB¡ÎEF£¬¾ØÐÎABCDËùÔÚµÄƽÃæºÍÔ²OËùÔÚµÄƽÃ滥Ïà´¹Ö±£¬ÇÒAB=2£¬AD=EF=1£®
£¨¢ñ£©ÇóÖ¤£ºAF¡ÍƽÃæCBF£»
£¨¢ò£©ÉèFCµÄÖеãΪM£¬ÇóÖ¤£ºOM¡ÎƽÃæDAF£®
¾«Ó¢¼Ò½ÌÍø

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨Àí¿Æ×ö£©ÈçÓÒͼ£¬¶àÃæÌåÊǹýÕýËÄÀâÖùµÄµ×ÃæÕý·½ÐÎABCDµÄ¶¥µãA×÷½ØÃæAB1C1D1¶ø½ØµÃµÄ£¬ÇÒBB1=DD1£¬ÒÑÖª½ØÃæAB1C1D1Óëµ×Ãæ³É30¡ãµÄ¶þÃæ½Ç£¬AB=1£¬ÔòÕâ¸ö¶àÃæÌåµÄÌå»ýΪ£¨¡¡¡¡£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨Àí¿Æ£©£¨13·Ö£©ÔÚÈçͼËùʾµÄ¿Õ¼ä¼¸ºÎÌåÖУ¬Æ½ÃæƽÃæABC£¬AB=BC=CA=DA=DC=BE=2£¬BEºÍƽÃæABCËù³ÉµÄ½ÇΪ60¡ã£¬ÇÒµãEÔÚƽÃæABCÉϵÄÉäÓ°ÂäÔÚµÄƽ·ÖÏßÉÏ.

£¨1£©ÇóÖ¤£ºDE//ƽÃæABC£»£¨2£©Çó¶þÃæ½ÇE¡ªBC¡ªAµÄÓàÏÒ£»

£¨3£©Çó¶àÃæÌåABCDEµÄÌå»ý.

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º2010ÄêÁÉÄþÊ¡½õÖÝÊи߿¼Êýѧ¶þÄ£ÊÔ¾í£¨½âÎö°æ£© ÌâÐÍ£º½â´ðÌâ

£¨Àí¿Æ£©ÈçͼµÄ¶àÃæÌåÊǵ×ÃæΪƽÐÐËıßÐεÄÖ±ËÄÀâÖùABCD-A1B1C1D1£¬¾­Æ½ÃæAEFGËù½ØºóµÃµ½µÄͼÐΣ®ÆäÖСÏBAE=¡ÏGAD=45°£¬AB=2AD=2£¬¡ÏBAD=60°£®

£¨¢ñ£©ÇóÖ¤£ºBD¡ÍƽÃæADG£»
£¨¢ò£©ÇóƽÃæAEFGÓëƽÃæABCDËù³ÉÈñ¶þÃæ½ÇµÄÓàÏÒÖµ£®

£¨ÎÄ¿Æ£©Èçͼ£¬ABΪԲOµÄÖ±¾¶£¬µãE¡¢FÔÚÔ²OÉÏ£¬AB¡ÎEF£¬¾ØÐÎABCDËùÔÚµÄƽÃæºÍÔ²OËùÔÚµÄƽÃ滥Ïà´¹Ö±£¬ÇÒAB=2£¬AD=EF=1£®
£¨¢ñ£©ÇóÖ¤£ºAF¡ÍƽÃæCBF£»
£¨¢ò£©ÉèFCµÄÖеãΪM£¬ÇóÖ¤£ºOM¡ÎƽÃæDAF£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸