2023年11月1日南京鼓楼八上数学期中评分标准【录入版】

参考答案评分标准的精神给分.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为直角三角形·······································∴∠ADC＝180°-∠CDB=90°··························································································4分AD2＋DC2＝AC2·················································································5分设AC＝x.则（x－5）2＋122＝x2··································································∴x＝16.9··············∴∠BDC=∠BEC＝90°··············································································1分∴EM＝BC，DM＝BC·······························∴EM＝DM································································即△DEM为等腰三角形·····································20本题8分）〈∠A=∠A，∴△ABD≌△ACE··········································∴∠ABD=∠ACE·······················································································2分∴∠ABC=∠ACB·······················································································3分∴∠ABC-∠ABD=∠ACB－ACE∴∠OBC=∠OCB（也可证△EBC≌△DCB得到该结论）···························4分∴OB＝OC··············∴点O在BC的垂直平分线上··················∴点A在BC的垂直平分线上····························································∴AO⊥BC··········································21本题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是等边三角形···································22本题8分）∴∠C=∠DBE＝90°··················································································〈lAB＝DE.∴Rt△ABC≌Rt△EDB（HL）·············································=BD－AC·························································································4分（2）连接AD、AE.APBQCDAPBQCD∴∠AOD=∠BDE+∠OBD=∠ABC+∠OBD=∠EBD＝90°··························∴SACBDb＋a）a=c2＋b（a－b）·············································································7分2＋b2＝c2································································23本题7分）（1）5·····························································································（2）角平分线正确2分，点D标正确1分··········································24本题8分）（1）二·························································（2）过点A作AM⊥BD，AN⊥CD，分别交BD、CD的延长线于点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本题9分）【问题解决】∴△DAE≌△DBC····································∴∠EAC+∠ACB＝180°···············································································3分∴∠EAC＝180°-∠ACB=90°=∠ACB∴AB＝EC····················································【问题再探】∴BD＝FD··············