初中經(jīng)典幾何證明練習(xí)題(含答案)-資料下載頁
2025-06-18 07:36本頁面
【正文】 GO+∠EFO=180176。∴E、G、O、F四點(diǎn)共圓∴∠GEO=∠HFG∵∠EGO=∠FHG=90176?！唷鱁GO∽△FHG∴=∵GH⊥AB，CD⊥AB∴GH∥CD∴∴∵EO=CO∴CD=GF2證明：作正三角形ADM，連接MP∵∠MAD=60176。，∠PAD=15176?！唷螹AP=∠MAD+∠PAD=75176?！摺螧AD=90176。，∠PAD=15176?！唷螧AP=∠BAD∠PAD=90176。15176。=75176?！唷螧AP=∠MAP∵M(jìn)A=BA，AP=AP∴△MAP≌△BAP∴∠BPA=∠MPA，MP=BP同理∠CPD=∠MPD，MP=CP∵∠PAD＝∠PDA＝15176?！郟A=PD，∠BAP=∠CDP=75176?！連A=CD∴△BAP≌∠CDP∴∠BPA=∠CPD∵∠BPA=∠MPA，∠CPD=∠MPD∴∠MPA=∠MPD=75176?！唷螧PC=360176。75176。4=60176?！進(jìn)P=BP，MP=CP ∴BP=CP ∴△BPC是正三角形3證明:連接AC，取AC的中點(diǎn)G,連接NG、MG∵CN=DN，CG=DG∴GN∥AD，GN=AD∴∠DEN=∠GNM∵AM=BM，AG=CG∴GM∥BC，GM=BC∴∠F=∠GMN∵AD=BC∴GN=GM∴∠GMN=∠GNM∴∠DEN=∠F1證明：（1）延長AD交圓于F，連接BF，過點(diǎn)O作OG⊥AD于G∵OG⊥AF∴AG=FG∵=∴∠F=∠ACB又AD⊥BC，BE⊥AC∴∠BHD+∠DBH=90176?！螦CB+∠DBH=90176?！唷螦CB=∠BHD∴∠F=∠BHD∴BH=BF又AD⊥BC∴DH=DF∴AH=AG+GH=FG+GH=GH+DH+DF+GH=2GH+2DH=2（GH+DH）=2GD又AD⊥BC，OM⊥BC，OG⊥AD∴四邊形OMDG是矩形∴OM=GD ∴AH=2OM（2）連接OB、OC∵∠BAC=60∴∠BOC=120176。∵OB=OC，OM⊥BC∴∠BOM=∠BOC=60176?！唷螼BM=30176?！郆O=2OM由（1）知AH=2OM∴AH=BO=AO2證明：作點(diǎn)E關(guān)于AG的對稱點(diǎn)F，連接AF、CF、QF∵AG⊥PQ ∴∠PAG=∠QAG=90176。又∠GAE=∠GAF ∴∠PAG+∠GAE=∠QAG+∠GAF即∠PAE=∠QAF∵E、F、C、D四點(diǎn)共圓∴∠AEF+∠FCQ=180176?！逧F⊥AG，PQ⊥AG∴EF∥PQ∴∠PAF=∠AFE∵AF=AE∴∠AFE=∠AEF∴∠AEF=∠PAF∵∠PAF+∠QAF=180176?！唷螰CQ=∠QAF∴F、C、A、Q四點(diǎn)共圓∴∠AFQ=∠ACQ又∠AEP=∠ACQ∴∠AFQ=∠AEP在△AEP和△AFQ中∠AFQ=∠AEP AF=AE∠QAF=∠PAE∴△AEP≌△AFQ∴AP=AQ第11頁共1
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