ÌâÄ¿ÄÚÈÝ

Èçͼ1£¬µãC½«Ï߶ÎAB·Ö³ÉÁ½²¿·Ö£¬Èç¹û
AC
AB
=
BC
AC
£¬ÄÇô³ÆµãCΪÏ߶ÎABµÄ»Æ½ð·Ö¸îµã£®Ä³Ñо¿Ð¡×éÔÚ½øÐпÎÌâѧϰʱ£¬Óɻƽð·Ö¸îµãÁªÏëµ½¡°»Æ½ð·Ö¸îÏß¡±£¬ÀàËƵظø³ö¡°»Æ½ð·Ö¸îÏß¡±µÄ¶¨Ò壺ֱÏßl½«Ò»¸öÃæ»ýΪSµÄͼÐηֳÉÁ½²¿·Ö£¬ÕâÁ½²¿·ÖµÄÃæ»ý·Ö±ðΪS1£¬S2£¬Èç¹û
S1
S
=
S2
S1
£¬ÄÇô³ÆÖ±ÏßlΪ¸ÃͼÐεĻƽð·Ö¸îÏߣ®

£¨1£©Ñо¿Ð¡×é²ÂÏ룺ÔÚ¡÷ABCÖУ¬ÈôµãDΪAB±ßÉϵĻƽð·Ö¸îµã£¨Èçͼ2£©£¬ÔòÖ±ÏßCDÊÇ¡÷ABCµÄ»Æ½ð·Ö¸îÏߣ®ÄãÈÏΪ¶ÔÂð£¿ÎªÊ²Ã´£¿
£¨2£©Ñо¿Ð¡×éÔÚ½øÒ»²½Ì½¾¿Öз¢ÏÖ£º¹ýµãCÈÎ×÷Ò»ÌõÖ±Ïß½»ABÓÚµãE£¬ÔÙ¹ýµãD×÷Ö±ÏßDF¡ÎCE£¬½»ACÓÚµãF£¬Á¬½ÓEF£¨Èçͼ3£©£¬ÔòÖ±ÏßEFÒ²ÊÇ¡÷ABCµÄ»Æ½ð·Ö¸îÏߣ®ÇëÄã˵Ã÷ÀíÓÉ£®
·ÖÎö£º£¨1£©Éè¡÷ABCµÄ±ßABÉϵĸßΪh£¬ÓÉÈý½ÇÐεÄÃæ»ý¹«Ê½¼´¿ÉµÃ³ö
S¡÷ADC
S¡÷ABC
=
AD
AB
£¬
S¡÷BDC
S¡÷ADC
=
BD
AD
£¬ÔÙÓɵãDΪ±ßABµÄ»Æ½ð·Ö¸îµã¿ÉµÃ³ö
S¡÷ADC
S¡÷ABC
=
S¡÷BDC
S¡÷ADC
£¬¹Ê¿ÉµÃ³ö½áÂÛ£»
£¨2£©ÓÉDF¡ÎCE¿ÉÖª¡÷DECºÍ¡÷FCEµÄ¹«¹²±ßCEÉϵĸßÒ²ÏàµÈ£¬¹ÊS¡÷DEC=S¡÷FCE£¬ÉèÖ±ÏßEFÓëCD½»ÓÚµãG£¬ÓÉͬµ×µÈ¸ßµÄÈý½ÇÐεÄÃæ»ýÏàµÈ¿ÉÖªS¡÷DEG=S¡÷FEG£¬¹Ê¿ÉµÃ³öS¡÷ADC=SËıßÐÎAFGD+S¡÷FCG=S¡÷AEF£¬ÔÙÓÉS¡÷BDC=SËıßÐÎBEFC£¬ÔÙÓÉ
S¡÷ADC
S¡÷ABC
=
S¡÷BDC
S¡÷ADC
¿ÉÖª
S¡÷AEF
S¡÷ABC
=
SËıßÐÎBEFC
S¡÷AEF
£¬¹ÊÖ±ÏßEFÒ²ÊÇ¡÷ABCµÄ»Æ½ð·Ö¸îÏߣ®
½â´ð£º½â£º£¨1£©Ö±ÏßCDÊÇ¡÷ABCµÄ»Æ½ð·Ö¸îÏߣ®ÀíÓÉÈçÏ£º
Éè¡÷ABCµÄ±ßABÉϵĸßΪh£®
¡ßS¡÷ADC=
1
2
AD•h£¬S¡÷BDC=
1
2
BD•h£¬S¡÷ABC=
1
2
AB•h£¬
¡à
S¡÷ADC
S¡÷ABC
=
AD
AB
£¬
S¡÷BDC
S¡÷ADC
=
BD
AD
£¬
ÓÖ¡ßµãDΪ±ßABµÄ»Æ½ð·Ö¸îµã£¬
¡à
AD
AB
=
BD
AD
£¬
¡à
S¡÷ADC
S¡÷ABC
=
S¡÷BDC
S¡÷ADC
£¬
¡àÖ±ÏßCDÊÇ¡÷ABCµÄ»Æ½ð·Ö¸îÏߣ»

£¨2£©¡ßDF¡ÎCE£¬
¡à¡÷DECºÍ¡÷FCEµÄ¹«¹²±ßCEÉϵĸßÒ²ÏàµÈ£¬
¡àS¡÷DEC=S¡÷FCE£¬
ÉèÖ±ÏßEFÓëCD½»ÓÚµãG£¬
¡àS¡÷DEG=S¡÷FCG£¬
¡àS¡÷ADC=SËıßÐÎAFGD+S¡÷FCG=SËıßÐÎAFGD+S¡÷DGE=S¡÷AEF£¬
S¡÷BDC=SËıßÐÎBEFC£¬£®
ÓÖ¡ß
S¡÷ADC
S¡÷ABC
=
S¡÷BDC
S¡÷ADC
£¬
¡à
S¡÷AEF
S¡÷ABC
=
SËıßÐÎBEFC
S¡÷AEF
£¬
¡àÖ±ÏßEFÒ²ÊÇ¡÷ABCµÄ»Æ½ð·Ö¸îÏߣ®
µãÆÀ£º±¾Ì⿼²éµÄÊÇÏàËÆÐÎ×ÛºÏÌ⣬Éæ¼°µ½Æ½ÐÐÏßµÄÐÔÖʼ°Èý½ÇÐεÄÃæ»ý¹«Ê½£¬¸ù¾ÝÌâÒâÀí½â»Æ½ð·Ö¸îµã¼°·Ö¸îÏߵĶ¨ÒåÊǽâ´ð´ËÌâµÄ¹Ø¼ü£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿
Èçͼ1£¬µãC½«Ï߶ÎAB·Ö³ÉÁ½²¿·Ö£¬Èç¹û
AC
AB
=
BC
AC
£¬ÄÇô³ÆµãCΪÏ߶ÎABµÄ»Æ½ð·Ö¸îµã£®Ä³Ñо¿Ð¡×éÔÚ½øÐпÎÌâѧϰʱ£¬Óɻƽð·Ö¸îµãÁªÏëµ½¡°»Æ½ð·Ö¸îÏß¡±£¬ÀàËƵظø³ö¡°»Æ½ð·Ö¸îÏß¡±µÄ¶¨Ò壺ֱÏßl½«Ò»¸öÃæ»ýΪSµÄͼÐηֳÉÁ½²¿·Ö£¬ÕâÁ½²¿·ÖµÄÃæ»ý·Ö±ðΪS1£¬S2£¬Èç¹û
S1
S
=
S2
S1
£¬ÄÇô³ÆÖ±ÏßlΪ¸ÃͼÐεĻƽð·Ö¸îÏߣ®
£¨1£©Ñо¿Ð¡×é²ÂÏ룺ÔÚ¡÷ABCÖУ¬ÈôµãDΪAB±ßÉϵĻƽð·Ö¸îµã£¨Èçͼ2£©£¬ÔòÖ±ÏßCDÊÇ¡÷ABCµÄ»Æ½ð·Ö¸îÏߣ®ÄãÈÏΪ¶ÔÂð£¿ÎªÊ²Ã´£¿
£¨2£©ÇëÄã˵Ã÷£ºÈý½ÇÐεÄÖÐÏßÊÇ·ñÒ²ÊǸÃÈý½ÇÐεĻƽð·Ö¸îÏߣ¿
£¨3£©Ñо¿Ð¡×éÔÚ½øÒ»²½Ì½¾¿Öз¢ÏÖ£º¹ýµãCÈÎ×÷Ò»ÌõÖ±Ïß½»ABÓÚµãE£¬ÔÙ¹ýµãD×÷Ö±ÏßDF¡ÎCE£¬½»ACÓÚµãF£¬Á¬½ÓEF£¨Èçͼ3£©£¬ÔòÖ±ÏßEFÒ²ÊÇ¡÷ABCµÄ»Æ½ð·Ö¸îÏߣ®ÇëÄã˵Ã÷ÀíÓÉ£®
£¨4£©Èçͼ4£¬µãEÊÇƽÐÐËıßÐÎABCDµÄ±ßABµÄ»Æ½ð·Ö¸îµã£¬¹ýµãE×÷EF¡ÎAD£¬½»DCÓÚµãF£¬ÏÔȻֱÏßEFÊÇƽÐÐËıßÐÎABCDµÄ»Æ½ð·Ö¸îÏߣ®ÇëÄã»­Ò»ÌõƽÐÐËıßÐÎABCDµÄ»Æ½ð·Ö¸îÏߣ¬Ê¹Ëü²»¾­¹ýƽÐÐËıßÐÎABCD¸÷±ß»Æ½ð·Ö¸îµã£®
¾«Ó¢¼Ò½ÌÍø

Î¥·¨ºÍ²»Á¼ÐÅÏ¢¾Ù±¨µç»°£º027-86699610 ¾Ù±¨ÓÊÏ䣺58377363@163.com

¾«Ó¢¼Ò½ÌÍø