Partial preview of the text
Download 8 grade exercise for students and more Exercises Mathematics in PDF only on Docsity!
Buster Ne 1 1) Haitre onpeyxenenue MHoroyrousHVka, BepIIMHEI, CTOPOHEI, (MaroHamu HM TepumeTpa MHOrOyrouIbHHKa. 3arMmmte POpMYIy CYMMBI yIJIOB BbIyKIOrO MHOTOYTOIBHUKa, 2) Chopmysmpyiite TeopeMsI 0 cpeqHuX JMHMAX TpeyroubHMka M Tpanequu. JloxaxxkuTe oAHY V3 HHX M10 BEIGopy. 3) Paguyc OB oxpyxkHocTH c WeHTpoM B TouKe O mepeceKaeT xopay AC B touxe D u mepnenguxynapen eit. Haltqute anMHy xopapr AC, ecnm BD=lcm, a panuye oKpyxxHocTH paper 5cm. 4) Tlepumerp npsmoyrombHuka papeH 56, a quaronans pasna 20. Haligure nmomags 9STOTO TIPAMOYTOJIBHUKa. Buner Ne 2 1) Cchopmynupytite ompeyenenue u cBoiicTBa Napamenorpamma. 2) Chopmysupyiire u JoKaxKuTe cBOMCTBO MeqMaH TpeyrombHuKa. 3) Tuaronam BD napannenorpamma ABCD o6pasyer c ero cTopoHamu yruEi, paBHBie 60° u 55°. Haiaute MeHbuMii yrom Mapamemorpamma. 4) Haiigute yron ACO, ecau ero cropona CA kacaeTca okpyxkHocru, a myra AD r r) c OKPY2KHOCTH, 3aKJHOUeHHad BHYTPH 3TOrO yrua, paBHa 100°. Buyer Ne 3 1) Cchopmynupyiire ompeyenenne u cBoiicTBa NprMoyrombHuKa. 2) Ccoopmynupyiite u qoKaxute Teopemy [Imdaropa. 3) Haiinute penmunny (B rpaqycax) BOMcaHHoro yrua a, omMparonjeroca Ha xopay AB, paBHyfo payuycy OKpyKHOCTH. 4) B tpeyronpyuxe ABC yrast A u C pasunt 20° 1 60° ‘ , cooTBetcTBeHHO. Haligute yrom Mexyy BbICcoTOH u BH vu 6uccextpucok BD. Buuet Ne 4 1) Chopmysmpyfite onpeyenenue u cBofcTBa pomGa. 2) Chopmysmpyiite u JoKaxkuTe Teopemy 0 BIIMCaHHOM yrne (sOGoi YacTHBLT cya) 3)B paBHobeypenHo Tpanennn W3BeCTHA BEICOTa, Gombitiee ocHOBaHHe M YTOul Ip OCHOBaHHH (CM. pHcCyHOK). 420 Haiigute Menbliiee OcHoBaHHe. 4) Orpesxu AB u DC sexaT Ha mapamienbHBIxX NpAMbIx, a otpeska AC u BD mepecekaroTca B TouKe M, Haiinute MC, ecnm AB=16, DC=24, AC=25. Brunet Ne 5 1)Cchopmynupytite ompegenenve tpanemmu. Ha3zopure Buybl Tpaneruu, saiite onpezeenve Kaxkqoro BHA. 2)Ccopmynupylire Hw TOKaxKHTe CBOMCTBO OTpPe3KOB KaCaTeJIbHbIX, MPOBeeHHEIX K OKPY2KHOCTH 43 ODHOM TOUKH. 3)Or cron6a K JOMy HaTAHYT IpoBod, KoTopsrit KpellwTca Ha BbICOTe 3M OT 3eMJIH (CM. PHCYyHOK). PaccTosune oT foMa Wo cTon6a 8M. BBIYMcCIMTe AIMHY mposoga. in 4) Buccextpucsi yrnos A u B pu Goxosoli cropoue AB tpaneyuu ABCD nepecexarores B TouKe F’. Hatigqute AB, ecnu AF = 24, BF = 10. Bunet Ne 6 1) Hatire onmpegzenenue mogoOusrx TpeyrombHuKos. Ha3zosute mpu3sHakH moyzobna TPeyTOJIBHUKOB. 2) Chopmysupylite npusHaku napamenorpamoa. (JloKaxuTe oJMH 13 HUX 10 BEIOOpy) 3) OcHospaHua Tpaneruu 12 u 25. Halinure Sonpummii u3 oTpe3KoB, Ha KOTOpsIe WeNHT Cpe{HIO!0 JIMHMIO STO Tpalelwuu Onna H3 es THaroHnaseit. 4) OxpyxxHocTh ¢ WeHTpom Ha cTopoHe AC tpeyrompyuxa ABC mpoxogur 4epe3 BepimmHy C u Kacaetca npsMoi AB s tTouxe B. Haitaure AC, ecum quamerp OKpyxHocTH paBeH 7,5, a AB=2. Buster Ne 7 1) flaiire onpeyenenue cunyca, KOcHHYyca HM TaHreHca OcTporo yrma psMoyrosbHoro Tpeyronbyuka. 3anummre dopMyEI COOTHOMeHHIi, OCHOBHOe TpHroHOMeTpHecKoe TOXKICCTBO 2) Ccohopmynupyiite u JoKaKuTe Teopemy 06 orHomeHuM Momazelt HOnOOHBIX ouryp. 3) Haiiqute rpanycuyio Mepy ZMON, ecuu u3pecTHo, NP- quametp, a rpatycHas Mepa Z MNP pasua 18°. a > 4) Karetsi mpaMoyrojpHoro TpeyrombHuKa paBHBr 15 u 20. Haiiqute spicoty, TIPOBeAGHHY10 K THIOTeHY3e. Buner Ne 8 1) Ha3opute 3HaveHua CHHYca, KocHHYyca MH TaHrenca yruios 30°, 45°, 60°. 8 1) Jaiite onpegenenue oxpyxXHocTn, BIMCaHHOM B MHOTOyTObHEK, MHOFOyrouIBHHKa, OnMcaHHOro OKOJIO OKpy2KHocTH. Ha3oBute cBolicTBO OMMCaHHOTO YeTbIPeXYroNbHUKa. 2) Chopmysmmpyiite u JoKaxKute cBoiicrBa Wuarovameii pomOa. 3) Tinomay napastenorpamma ABCD pasua 60. Touxa E — cepeguna croponsr AB. Haliqure noma, Tpanenuu DAEC. 4) Oxpy>xHocTs mpoxoguT 4epes BepummHE! A u C TpeyrombHuka ABC u nepecexaert ero cropousi AB u BC B Ttouxax K u E cooTsercrsenuo. Otpesxu AE u CK nepneHankyapHel. Hatiqure Z KCB, ecnm 2 ABC=20°. Buster Ne 13 1) Aatire onpeyenenve oKpyxKHOCTH, omMcaHHOH oKOIO MHOroyrouBHuka, MHOPOYTOJIBHUKa, BIIMCaHHOrO = B OKpy2XHOCTb. Ciopmymupyiite cBolicTBo YeTbIPCXYTOJIBHUKA, BIIMCaHHOrO B OKPY2KHOCTB. 2) Ccoopmysmpylite u ToKaxute cBoiicTBo OucceKTpucHl yrma. 3) B mpsmoyrombHoM TpeyroubHUKe OfMH M3 KaTeTOB paBeH 10, a yron, nexannit HallpOTHB Hero papex 45°. Hatiqute nomayb TpeyroubHuKa. 4) Buccextpucri yrnop A u B napannenorpamma ABCD nepecexatotca B Touxe K. Haliqure nmomanb napanuenorpamma, ecm AD=19, a pacctosHue or Touxn K 70 cTopous! AB paBuHo 7. Bunet Ne 14 1) Cchopmysupyiite Teopempl 06 yrmax MexKAY KacaTeNbHOl uM xopyoli, Mexny DByMs XOplaMM, MEXKTy JByYM# CeKyIIMMH. 2) Cchopmynupyiite u oKaKuTe CBOMCTBO yrioB MpH OcHOBaHMM paBHOOespeHHolt Tpanelun. 3) Cropona papnoctoponHero TpeyrompHuKka papa 16V3. Haiiqure MeqMaHy 9TOrO TpeyroubHuka. 4) Buccextpuca yria A mapannenorpamma ABCD nepecexaet ero cropony BC B touxe E. Hatigute nnomab napanmenorpamma ABCD, ecu BE=7, EC=3, 2 apc=iso. Bunet Ne 15 1) Chopmysmpyiite teopemy Pameca, Teopemy 0 MponopuMOHaJIbHBIX OTpesKax. 2) Chopmymmpyiite 4 JoKaxkuTe CBOMCTBO OTPe3KOB MepeceKarouuxca Xopy. , 3) Cropoua pom6a paBHa 34, a ocTppili yrom pape 60°. Btcora pom6a, onymeHHad 13 BeplIMHBI Tymoro yrula, WemHT cTopoHy Ha Ba oTpe3Ka. KakoBbl JIMHbI 9THX OTpe3KOB. 4) Touxa H spnsetca ocHopasuem BsicoTs! BH, mpopexeHHol u3 BeplIMHI NpaMoro yrma B mpsmoyrojbHoro TpeyrombHuKa ABC, OxpyxHocTb c yuamMetpom BH TlepecekaeT cropousi AB u CB B TouKax M u F cootsetctseuuo. Haliqute yiuny MF, ecm BH=15. TIpunoxenne Ne 3 Kputepuu OUCHHBAaHHA H WikKasla Tepeposa 6asI0B B DIKOJIBHYIO OTMEeTKy permouasIBHOrTO my6M4HOrO 3aueTa 110 reOMeTpHH Ne Bormpoca Ilkana ovjeHuBaHua oT 0 go 1 6anna ot 0 no 2 GannoB or 0 go 1 Oana B] WwW] w]e ot 0 40 2 Oans0B 3a oTBeT Ha Bompoc Ne 2 BpictapnaioTca 2 Oana, ecu ccbopMymuposana TIpaBHIbHO TeopeMa H wpeycTapieHo e&€ joKa3arempcTBo; 1 Gaz, ecu ccbopMyHpoBaHa M1paBubHO Teopema 6e3 TOKa3aTeECTBa, U 0 OamIOB BO BCeXx Upyrux coyyasx. Orser na Bompoc Ne 4 (sanjaya), olleHHBaeMBIli AByMa Oannamu, cuMTaetca BBINOIHCHHBIM BePHO, eC BbIOpaH MpaBMJIbHbIii MyTb pellieHuA, NOHATeH MyTb paccyKTeHHs, aH BepHprli orpet. Ecnm Jonymena ommOxa, He Hocauas IPHHUMIMaNbHOrO XapakTepa HW He BIIMMOIIad Ha OOMyIO MpaBHIbHOCTb xota pelleHua, To BbICTaBIAeTca Ha 1 Ga MeHBIIe. MakcumasbHoe KomM4ecTBO OaloB — 6 GammoB. Ilkana nepesoya 6ammoB B INKOJIBHYIO OTMETKY PerHOHAJI_HOrO NyOMM4HOrO 3a4eTa TO reOMeTpHU Ormetxa Ilepecnaua «3» «4» «5» Bann 0-2 3 4 5-6 *TIpy ycuIOBMH, yTO pelleHa ogHa u3 3ayat 
