人教版几何模型基本图形

1、1EDFABAB/CD2ABEAEECDBCEBAAB/CDDEBDE360CFCBC7CABCBDDBDABBOCA84AO90EBBCAAAODE/BCBOCEBCA9BOCB190A2DBEO5AEDB5E打学习BEC条件可 CAGJ .CC10. ABG丄CE注 换成 BAE 为等腰Rt OD = OEAE = 2BDAC = BC 丄BD ACEDCB; ACMDCN MCE注： BCE绕C旋转时正方形 ABCD 中BO = EO+CO , OM+ON = CO , OC 平分/ AOB结论有些变化.BE+CD = BCEC FCBD 丄 CE BD=CE平移后也成立BE、CD相交所

2、成锐角为60°B DC ADE = AB+ACAC = BC DEF为等腰RtABDE与ACFG为正 方形 EC = BG ,3. a，贝U CECE = BDNCB; AE = BD, AM = DN , EM = BN , CM =CN , AE、BD 相交成锐角 60° AO = DO+CO , AD平分/ DE/AC ; AEDE中，知二推一 ABD , ACE 为等 边厶 BE = CD ABC为等腰Rt, AE 平分/ CAB , / D6. D-A2C DAACD、 BCE 为等边, A、C、B 共线90 1C FBDDCPB+PC = 2PD/ ABP+ /

3、 C= 180AD = CDCD = BDAD = BD12.AB = ACAE+BE = BCCD = CE = BGCEFD为菱形AC = BC/ ADC =Z BDF ;CF+DF=ADDE+BF = EFAE 平分/ DEF, AF 平分/ BFE/2=2/ 1AF = BC+CF/ A =Z B或/ A+ / B = 180ADAB = ACDE+DF =BM钝角也成立CC等腰梯形EF+EG = CMAE+CF = CDEF= 2 OES四边形OEBF = a24BE+DF=AEABF=ADDBF=ACBF 丄 ADBF 丄 AC中点四边形少是二，取决于AC、 BD的关系， 的关系对

4、应的关系EFGHEF,AC、E至27.AEHBD/ 1 = Z B ADCCDBACBac2=ad-abBC2= BD- BAAC-BC = AB-CDCD2 = AD- BD/ C = Z D ABC ADEAB-AD = AC-AE/ B = Z E ADE ACBAD-AB = AC-AEA梯形ABCD AE =BE; AD+BC = CD ; DE丄CE，知二推一中:DCDF = EFB23.BAM 2+BN2= MN 2AD = BC = a, BF = CFHF+HD = aEF/AD1EF = - (BC AD)2AE 2AFED BFED C/ 1 = Z C ADEACBAD

5、-AB = AE-AC/ 1 = Z B30.E M FAN DGAM BC ADC s acb /ADC =Z ACBAC 2=AD ABDE/BCDN = EN , BM = CMMO = NO1 1 2AD BC MNDM BNEM CN 当DM = EM时, 那么 BN = CNAO = 2DOBO = 2EOCO= 2FONAB BM BNAC CM CN37BAOD2 DE2 a2OD2 DE2 a2同上33.1 1 1AB CD EF34.AD = DC , PN/BDPN+MN =2BDAB = ACPE+PF= 2AD半弧所对的圆心角等于整弧所对的圆心角AOC APB1五元素

6、：CD过圆心O;CD丄AB :AM = BM ;AD= BD :AC=BC中，知二推三。注：由推另三，需附加条件AB不是直径。2图形中弦长、半径、弦心距、弓高两个量，那么另 二可求。EC FDAE FGAE BF 2OM假设 AB、EF 相交，那么 |AE BF|= 2OMEC FCAE FGAE BF AB1C 180 AOB25.共斜边的两直角三角形，四个顶点在同一圆上。CACD / EF 任意两边之积等于第三边上的高与其外接圆直径之积。如：AB AC = AD 2R钝角也适用；BC 正弦定理：一C2R不能直接用，可构造以直sin BAC径为斜边的Rt，利用三角函数求。1 OE BC2FM

7、的延长线平分ACAM CM FM AC = EC1CD AE2AC2 AM - AE AD AB1 OM -BF210C11BD CD ABE adc s CDE ABD s AEC s BED BD2= CD2= DE DAAB AC = AE AD AE DE = BE CDAB ACAD2cos BAD假设I为厶ABC内心，那么 BT = CD = ID，关注/ BAC为特殊角时图形的特殊性、及相关比值。12HD FD CH 丄 ABH点关于AC的对称点在圆上，H点关于AB的对称点在AB上,1OM -AH2BD = CD AD 平分 CAE13AD丄CD :AC平分 DAB ;DC切O

8、O于C中，知二推一。14PDPO PM PN PDM PNOCA 平分/ PCD OND OPN15A1BOC 90 A2BO DEr 2S ABC /C ABC1DEF 90- A216R18abr 竺注AC与BC不一定相等 a bBO OA :RQ切O O于Q。 RP = RQ中，知二推一OR可上、下平移，Q也可在AB上AB+CD = AD+BCAHD192 2APBP r OP2 2PAPB OP2 r2AE BFCG DGC Pde PA PB1DOE (180 P)2BE BD PBDpce PBEs pad PBA s PCBBE BD = AD CE假设AC是直径，那么 ADP = 45°*假设 BDE为等腰Rt或等边时，上述结论有些变化。23CAOiDO2BAC EC CB