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CHuven Ticp iir TRirc ounn SHRG SUV Dien TRDNG DAY HOG HINH HOC KHONG GIAN LOP 11 O ThS, PHAN A N H TAI" - PGS.TS, NGUYEN V A N L O G " a trung hpc phd thong (THPT), day hoc hinh hpc khdng gian (HHKG), ngudi hpc khd ed t h i Hi gidc dupe neu thilu di nhimg hinh dnh true quon Viec sudyng md hinh true quan dpy hpc phdn HHKG d Idp 11 dd Idm cho gid hpc sinh ddng, hoc sinh (HS) de h i p thu kiln thirc hon Tuy nhien, neu gido vien (GV) khoi thdc khdng hpp If cdc hinh dnh Hue quon, khdng kit ndi dupe ede hinh ve vdi d l phdt Hiln H/ cho HS thi gid hpc se rcri n x , l^m hieu qud D l qud Hinh chuyen filp h> trye quan semg suy dien Hong dpy hpc HHKG phdt huy dupe ndng luc gidi quylt vdn de eua HS, theo chung toi, GV cdn td ehi/c day hpc theo gial doqn k l H ^ dudi ddy: G i a i d o q n : «Truc q u o n ' O gioi doqn ndy, di hinh thdnh vd phdt t r i l n ndng lye tudng tt/png khdng gian cho HS, GV cd the hi/dng ddn HS gidl he thdng cdc bdi tdp (BT) tinh hud'ng thdng quo cdc dpng todn sou: Dqng 1: Cdc BT HHKG nhdm hinh thdnh b i l u h/png trye quon dt/a Hen cdc ddi H/png eo bdn: d i l m , dudng thdng, mat phdng duo Hen md hinh quen thudc nhu: t u d i e n , hinh chop, hinh hop, O dqng BT ndy, cdc hinh hinh hpc dt/pc b i l u dien bdi quy udc «nhin thdy" hoy «che khud't" BT I: Cho h/ dien ABCD bieu dien bdi hinh I Hdy xdc djnh ede eqnh bi «ehe khud't", eqnh «nhin thdy", mat bj «ehe khud't", mat «nhin t h d / ' cua tu dien Hinh BT ndy nhdm giOp HS tudng tupng hinh khdng gian dua tren hinh b i l u dien phdng eiia K/ dien Tap chifiiaodue so (ki a • la/aoi D BT 2: Cho tu dien ABCD bleu dien bdi hinh Hdy neu cdc d i l m , dudng thdng, mdt phdng xdc djnh bdi tu dien BT yeu cdu HS k l ten cdc diem, dudng thdng, mdt phdng, Hjy nhien gidi, HS thudng ehi neu ede d i l m A, B, C, D; cdc dudng thdng AB, AC, AD, BC, BD, CD; cdc mat phdng (ABC), (ABD), (ACD), (BCD) md khdng chi ro cdc d i l m ndm tren dudng thdng chua cqnh vd mdt phdng chira cdc mat Clio tu dien, dudng thdng thudc mat phdng chira cdc mdt cua h/ dien Dqng 2: BT hinh thdnh mdi lien he khdng gian giOa cdc diem, dudng thdng, mat phdng vd giua cdc hinh khdng gian BT 1: Cho tl/ dien ABCD, diem M thupc cpnh CD Hdy cho biet diem M thupc cdc mat phdng ndo? (hinh 2) Khi gidi BT ndy, «ldi" md HS thudng mdc phdi Id Hm thieu Hong mat phdng (ACD) hope (BCD) Tucmg h/, ta cd BT sou: BT2: Cho Kr dien ABCD, dudng thdng AB thupc cdc mdt phdng ndo? Dqng 3: BT hinh thdnh b i l u tuqng khdng gian v l vj trf tuong dd'i glCfa d i e m , d u d n g thdng, mdt phdng BT 1: Cho tu dien ABCD: a] Hdy neu cdc cap dudng thdng edt chira cdc cpnh cua h/ dien; b) H d y neu ten ede c a p dudng thdng cheo chua ede eqnh cua h/ dien Khi gidi BT ndy, HS se Hi gidc khdng gian sai cho rdng, cdc cap di/dng thdng B nhu AC vd BD Id edt Vdi moi BT, ed t h i tdng dp Hinh phi/c tap cua hinh Ijdng cdch: riioy h/ dien bdi hinh chop h> gidc, hinh ch6p ngu gidc, * Tnriing fiai hoc Sai Con ** TnSUng Dai hoc sU pluni TP Ho Chi Minh BT 3: Cho tt> diSn ABCD, G Id Hong tdm tam gide BCD Xdc dinh cdc dudng thdng cheo vdi dudng thdng A G (hinh 3) Vdi BT d trSn, ndng lye h/dng tuqng khdng gian euo HS ddn dupe hinh thdnh, tpo co sd de phdt t r i l n ndng lye gidi todn cho HS, ddng thdi giup cdc em bt/dc ehuyln Hip sang gial doan O l gidl bdi todn ndy, HS cdn ed khd ndng trye quan d l tdch mp(ABD) ro vd si/ dyng djnh ff ve dudng trung binh cua tam gidc BT 2: Cho tu dlSn ABCD, gpl M , N Idn lupt Id tdm cdc tam gidc ABC, BCD Chung minh M N / / A D (hinh 6) rinu2 Glaf d o q n : «Trye quon - suy d i l n * O gial dopn ndy, hinh thdnh vd phdt H l l n ndng lye h/dng iuang khdng gian cho HS chuyin tu nhdn dqng cdc dd'i h/qng sang nhdn dqng quan h§ todn hqe Irfin hinh ve Cy t h i Id, IrSn co sd b l l u Hinhd ^ ^'"^^ tupng trye quon v l d l l m , dudng thdng, mdt phdng, quon he \\%n thudc, edn chuyen t i l p sang Di gidl BT 2, tu gid t h i l t d d cho, HS phdl \6dt\ nhdn dpng quan hS todn hoc Trudc h i t , GV Hio mdt phdng chira dudng thdng M N ro xet rISng Hln d l cho HS gidl todn thdng qua h3 thdng cdc Duo vdo tfnh chd't v l trpng tdm euo tam gide se bdi tdp sou: giup HS llSn tudng tdi djnh If Ta-tet, h> dd HS Hm 87" / : Cho h> dl&n ABCD, gpi M , N Idn lupt Id dupe cdc edeh gidl khde Hpng tdm cdc tam gidc ABC, BCD Xdc djnh vj trf ti/ong dd'i gluo dudng thdng M N vd ede dudng thdng chua eqnh cua h/ dien (hinh 4) Cdch (hinh d) Gpi E, F Idn lupt Id giao dllm Clio BM vdl AC, BN vdl CD Theo gid thilt M, N tdn lupt Id trpng tdm ciia cdc tam gide ABC, BCD nSn BE, BF Id trung tuyin cua cdc torn gidc ndy, suy E, F tuong ung Id Hung d l l m ciia cdc canh A C , CD Do d d , EF Id dt/dng Hung binh cija tam gide ACD, ta dupe: EF / / A D (1) Theo Hnh chdt trpng tdm eua tam gide thi: ^ Khi gidi bdi tdp ndy, HS cd t h i mdc sol Idm cho rdng hoi dudng thdng M N vd A D cheo BT 2: Cho tu dien ABCD, goi M , N , P, Q Idn luot id trung diem cdc canh A C , A D , BD, BC; ndi M N , NP, PQ, Q M (hinh 5) Hdy xdc djnh cdc dudng thdng song song vdi: a) M N ; b) M Q Khi gidi bdi tdp ndy, HS hoy bd sdt quan he song song cua ede cap dt/dng thdng M N vd PQ, M Q vd NP Tl/ mdi quan he song song, HS quon sdt hinh ve, sou d d lap ludn cd logic dua tren cdc djnh nghla, djnh If dd b i l t d l gidi quyet vdn d l Giai d o q n : «Suy d i e n ' Gioi dopn ndy hinh thdnh vd phdt H i l n ndng lye gidi q u y l t vdn di cho HS qua vlee gidi BT HHKG bdng eon dudng suy dien vdi djnh hudng tu theo cdc cdch sou: Cdch I: Su dyng hinh dnh trye quon, tach ede hinh phdng Hong khdng gian ro xet rieng, sou d d dCing k i l n thuc hinh hqc phdng d l gidi bdi todn ST f: Cho h/dten ABCD, go I M , N Idn lupt Id Hung d l l m cdc eqnh AB, AD Chung minh: M N / / BD = ^ f = ^ ] , dp dyng dinh If Ta-let tom gidc BEF, ta duoc: M N / / EF (2) Tu (1) vd (2), suy ro M N / / AD Vdi edeh gidl 1, mdt phdng (BEF) vd (ACD) dupe tach ro, sou d d Idn lirpt st/ dyng dinh If Talet vd tinh chdt vi dirong trung binh Hong tam gidc d l gidi q u y l t vd'n d l Vl@c ehung minh M N / / A D phdl d y a vdo dudng thdng thu Id EF Tuy nhifin, vdl cdch H i p edn sou, ta cd t h i tach ro mdt mdt phdng nhdm xdc djnh dupe Hue t i l p mdi quon he song song giua M N vd AD: Cdch (hinh 7): Do M Id Hpng tdm cua tam gidc ABC, nen dudng thdng A M edt BC Iqi Hung d i l m KeiJa cqnh B C v d ^ - | { l ) D o N Id Hpng tdm eua torn gidc BCD, nen Hung h j y i n DK di qua i{2).Tu(l),{2),suyro: KD A p dung dinh If Ta-let cho tam gidc KAD, ta ed: M N / / A D Q u a hai cdch gidl tren, cho thcfy: Vdi cCing mpl dCr kien, gid thiiylt euo bdi todn, ed the ton tqi n h l l u cdch k i t hpp khde don tdi ((dd Tap chi Slao due s6 tki a - la/aonj phue tqp" ciia cdc cdch gidi cung khde Vdl Cd t h i noi, qud trinh GV tqo ro cdc chuoi BT edeh , BT di/oe xem Id thdnh phdn cOa BT , t h i hien Hnh chdt eOa mdi giai doqn qud Hiy nhien, cdch gidl trye Hep vd «dep" hon trinh chuyen h> true quan song suy dien nhdm phdt trien ndng tyc gidl q u y l t vdn de cho HS cdch gidi BT 3: Cho tu dien ABCD, gpl M , N tdn lupt Id gidi cdc BT HHKG; viec xac djnh di/qe gid thuylt moi bdi todn se ho trq HS tu d l Hung d l l m euo ede canh hinh thdnh bleu tuqng true quan mdi, phdt trien AB, A D (hinh 8) Lay tu sdng tqo cho ede em Q d i l m K thudc canh BC, mp(MNK) edt CD tai F Chung minh K F / / M N Tdi li^u t h a m ktiio V d i BT n d y , tudng NX, Laylex Ndng luc tri tuS vi Ivra t u l i NXB tt/png trye quan euo HS Gfdorffic, H 1978, phdi chuyen H/ tri gide DoDn Qujinh (tdng chii hiCn) Hinh HQC 11 nSng Hinh «bd phdn" song Hi gidc cao, NXB Gido due H 2007 «tdng t h i " HS phdi b i l t tdng hop mdi quon h§ euo mat phdng: (MNK), (ABD), (BCD), xdc dinh 5UMMARV giao hjyIn ciia Krng cap mdt phdng, k i t hqp Thispc^er refers to form the problem solution ability vdl gid t h i l t M N Id dt/dng trung binh cua tam to students In teaching space geometry for the 11"" gidc ABD, dp dyng tfnh chdt v l giao hjyen cua grade of upper secondary sctiool wtvch is ckxe rioted to soti/ing the relation befv/een visual, deduction and mat phdng d l rut ro k i t ludn KF / / BD thought activity Nhimg yeu to dac thu (Tiip theo trang 13) ndng cao v l muc dp ndm vCrng KNGT cho ddi ngu CBLDCCS d tinh Bde Kqn • H O I THI I H f THAO HQC SINH KHUYfT TAT TOAN QUOC l i N THlJ IV {khoi mgt ngoy / / ! ) tgi TP ThiJi Binh, viti si; thorn gia ciia 12 dottn, gdn 500 van dOng vien (thui}c cdc Sd GODl, cdc Trung tam glDo due \\k ktiuyet tot: Hd NOI, Bd Ria - Vung Tdu, Do Ndng, Ddng Nai, Lang An, Qudng Binh, Qudng NgQi, Qudng Trj, Tfidi Nguyen, Phu Yen, Hdi Phdng, Thdi Binh) dd \i\ thuc tdt dep ngdy / / 1 Thu trtrdng BO GO-flT Trdn Quang Quy dd tliatn dv Lg khai mgc vd Le b^ mgc HiJi Ihi HOi thi Idn ndy, cac VOV ttonh Idi d mOn: Didn kinh - Chgy; Cd vuo; Bdng dd mini nam; K6o co; Cdu Tai lieu t h a m khao Dko Thi Ai Thi KI ndng giao tiip cua ddi nga cdng chiic hdnh chinh chuong trinh edi cdch hdnh chinh nhd nude Viit Nam LuSn an ti^n si, H^ NOi, 2007 DSng Phuemg Kiftt - NguySn Khic Vien TSm li Iioc va doi sffng NXB Khoa hoc xa hdi H 1994 Dai hgc Bob Jones, Hiiu qud vd qudn li truyin thdng BJU Press, Hoa Kl 2011 Ho&ng Anh Kindng giao tiip cQa sinh viin supham Loan an ti^n SI, Hk NOi 1992 Nguyin Van D6ng Mdt sdddc diim giao tiip ngodi gidng du&ng cua sinh viin Luan an ti€n sT, Ha N6i 1996 Phan Trpng Ngp (chu bifin) Tam If hoc tri tu# NXB Dgi hpc suphgm Hd Ndi 2001 VQ Dong (chii biftn) Tam li hpc xa hdi NXB Khoa hgcxd hdi H 2000 long; Bdng bdn Ket qud todn ioan: Nhdl: dodn Qudng Binh (37 huy chtrong: 14 HCV, 10 HCB, 13 HCfl) Nbi (fofffl:dodnfldng Noi (19 HC: 11 HCV, HCB, HCD) Ba: dodn Thdi Binh (31 HC: HCV, 15 HCB, HCD) B6n cqnh cdc gidl dtrg'c trao, BTC vd cdc nhd tci \jq cdn ttoo mOt sd hoc bdng vd sd lilt kiem cho cdc em HS cd thdnh tich coo Igi HOi thi P-V SUMMARY Based on specific surveying results, the author raises some typical factors influencing communication skills of grass-root leaders in administrative management in Bac Kan: people's acadenvc level: peoples'customs and tD^xjviors: people's level of Vietnamese language; minority ethnic people's knowledge and social relation skills; etc From these factors, the authors raise the demand for training to Improve the level of communication s«s of grass-root leaders h minorifyethrHC areas Tap chifiiaodue so (ki a la/aon) ... o q n : «Trye quon - suy d i l n * O gial dopn ndy, hinh thdnh vd phdt H l l n ndng lye h/dng iuang khdng gian cho HS chuyin tu nhdn dqng cdc dd''i h/qng sang nhdn dqng quan h§ todn hqe Irfin... khdng gian euo HS ddn dupe hinh thdnh, tpo co sd de phdt t r i l n ndng lye gidi todn cho HS, ddng thdi giup cdc em bt/dc ehuyln Hip sang gial doan O l gidl bdi todn ndy, HS cdn ed khd ndng trye quan. .. dudng thdng, mdt phdng, quon he \\%n thudc, edn chuyen t i l p sang Di gidl BT 2, tu gid t h i l t d d cho, HS phdl \6dt\ nhdn dpng quan hS todn hoc Trudc h i t , GV Hio mdt phdng chira dudng thdng