2023年11月1日南京鼓樓八上數(shù)學期中評分標準【錄入版】

參考答案評分標準的精神給分.123456BDACDB∴∠AFB=∠DEC······················································································1分∴BE＋EF＝CF＋EF·····································································∴BF＝CE················································································∴△ABF≌△DCE······································································∴∠B=∠C······························································································5分∴AB∥CD·························································BC2＝132＝169··························2＋BD2＝BC2·············································································即△BCD為直角三角形·······································∴∠ADC＝180°-∠CDB=90°··························································································4分AD2＋DC2＝AC2·················································································5分設AC＝x.則（x－5）2＋122＝x2··································································∴x＝16.9··············∴∠BDC=∠BEC＝90°··············································································1分∴EM＝BC，DM＝BC·······························∴EM＝DM································································即△DEM為等腰三角形·····································20本題8分）〈∠A=∠A，∴△ABD≌△ACE··········································∴∠ABD=∠ACE·······················································································2分∴∠ABC=∠ACB·······················································································3分∴∠ABC-∠ABD=∠ACB－ACE∴∠OBC=∠OCB（也可證△EBC≌△DCB得到該結論）···························4分∴OB＝OC··············∴點O在BC的垂直平分線上··················∴點A在BC的垂直平分線上····························································∴AO⊥BC··········································21本題8分）∴∠BAE+∠EAC=∠CAD+∠EAC∴∠BAC=∠EAD·······················································································2分∴∠AED=∠B＝60°···············································································∴∠ADN=∠ACM，DE＝BC········································································4分∴AM＝AN，∠MAC=∠DAN.············································∴∠MAN=∠MAC+∠CAN=∠DAN+∠CAN=∠DAC=60°··························································································7分∴△AMN是等邊三角形···································22本題8分）∴∠C=∠DBE＝90°··················································································〈lAB＝DE.∴Rt△ABC≌Rt△EDB（HL）·············································=BD－AC·························································································4分（2）連接AD、AE.APBQCDAPBQCD∴∠AOD=∠BDE+∠OBD=∠ABC+∠OBD=∠EBD＝90°··························∴SACBDb＋a）a=c2＋b（a－b）·············································································7分2＋b2＝c2································································23本題7分）（1）5·····························································································（2）角平分線正確2分，點D標正確1分··········································24本題8分）（1）二·························································（2）過點A作AM⊥BD，AN⊥CD，分別交BD、CD的延長線于點M、N·············3分NBNBAA DEM∠BDE DEM∴∠ADM=∠AND∴△AMD≌△AND········································∴AM＝AN，MD＝ND··························(AM＝ANlAB＝AC.∴Rt△AMB≌Rt△ANC（HL）·················25本題9分）【問題解決】∴△DAE≌△DBC····································∴∠EAC+∠ACB＝180°···············································································3分∴∠EAC＝180°-∠ACB=90°=∠ACB∴AB＝EC····················································【問題再探】∴BD＝FD··············