全等三角形提高32題含答案

1、 ABC旦ADAEAD=AB=522.證明AB=ACABC是等腰三角形ZB=NC又ME=MF,ABEM和ACEM是直角三角形BEM全等于ACEMMB=MC23.證明：NACB=90,NACD+NBCE=90,而AD丄MN于D,BE丄MN于E,/.ZADC=ZCEB=90,ZBCE+ZCBE=90,NACD=NCBE.在RtAADC和RtACEB中，ZADC=ZCEBZACD=ZCBEAC=CB,RtAADC今RtACEB(AAS),AD=CE,DC=BE,DE=DC+CE=BE+AD；不成立，證明：在AADC和ACEB中，ZADC=ZCEB=90ZACD=ZCBEAC=CB,ADCACEB(A

2、AS),AD=CE,DC=BE,DE=CECD=ADBE；證明AE丄ABNEAB=NEAC+NCAB=90度AF丄AC/.ZCAF=ZCAB+ZBAF=90度/.ZEAC=ZBAFAE=ABAF=ACEAC今AFABEC=BFZECA=ZF(2)延長(zhǎng)FB與EC的延長(zhǎng)線交于點(diǎn)GVZECA=ZF(已證)NG=NCAFVZCAF=90度EC丄BF25.證明：(1)BE丄AC,CF丄ABNABM+NBAC=90,NACN+NBAC=90/.ZABM=ZACNBM=AC,CN=ABABM旦ANACAM=AN(2)ABMANAC/.ZBAM=ZNZN+ZBAN=90NBAM+NBAN=90即ZMAN=90

3、AM丄AN26.連接BF、CE,證明ABFADEC(SAS),然后通過四邊形BCEF對(duì)邊相等的證得平行四邊形BCEF從而求得BC平行于EF27.在AB上取點(diǎn)N,使得AN=ACZCAE=ZEAN,AE為公共邊，/.ACAEAEAN/.ZANE=ZACE又AC平行BDZACE+NBDE=180而ZANE+ZENB=180/.ZENB=ZBDEZNBE=ZEBNBE為公共邊，/.EBNAEBDBD=BNAB=AN+BN=AC+BD28.證明：AD是中線BD=CDDF=DE,ZBDE=NCDFBDEACDFNBED=NCFDBECF29.證明：DE丄AC,BF丄AC,ZDEC=ZAFB=90,在RtD

4、EC和RtBFA中，DE=BF,AB=CD,RtADEC今RtABFA,ZC=ZA,ABCD30.結(jié)論：CEDE。當(dāng)ZAEB越小，則DE越小。證明：過D作AE平行線與AC交于F,連接FB由已知條件知AFDE為平行四邊形，ABEC為矩形，且DFB為等腰三角形。RTBAE中，NAEB為銳角，即ZAEB90DF/AE.ZFDB=ZAEB45RTAAFB中，NFBA=90-ZDBF45ABAFAB=CEAF=DECEDE31.先證明ABC今ABDC的出角ABC=gDCB在證明ABE9ADCE得出AE=DE32.證明：作CG平分NACB交AD于GZACB=90/.ZACG=ZDCG=45VZACB=90AC=BCAZB=ZBAC=45/.ZB=ZDCG=ZACGCF丄ADZACF+NDCF=90VZACF+ZCAF=9