Sáng tạo "Bài toán mở" trong dạy học hình học về quan hệ song song trong không gian ở trung học phổ thông

UE m "BAI TOM M f TROl DAY H0(] Hi l HOC

O TtiS. NGUYEN SON HA"

Phdn \dn, nhOng bdl todn ddl vdi hqc sinh

|HS| phd thSng hiin noy Id cdc bdi todn cd

kit ludn rdt cv thi, to gqi Id 'bdl hdn ddng".

Nhu^c dilm cua cdc bdl todn ddng Id hqn chl

khd ndng sdng tqo cOa HS. Theo G.Polyo, trudc

Hin, khi HS bai dSu vdo cdng v/ic, /lA' dl nghl

hq dl/ dodn kit qud ho0c chl m^t phdn ndo dd

aja kit qud. €i qud trinh dgy hgc dqt kit oud

coo, HS cdn V ""dm phd klin IhOc Irong fed

ndng cd thi, hdy cho phip HS h/ khdm phd HI

miic nil da Irong nhOng hodn cdnh a/ thi (1).

Xudt phdt h> ludn dilm ndy, xit nhOng bdi todn

ngut^c Iql so vdl bdl todn ddng Id bdl lodn md.

Mdt sd ddc dilm cOo bdi hadn md h-ong dqy

hqc todn d hvdng phd thing dd Id: Niu Id bdi

todn Hm 161 thi diiu phdl Hm khdng duqc niu lin

mdt cdch rd rdng vd tudng minh, HS phdl Hm tdt

cd cdc kit qud cd thi cd. Nlu Id bdl todn chOng

minh thi HS phdl dv dodn, phdt hlin ro cdc kit

qud cdn chOng minh; HS cd thi thoy ddl mdt sd

dliu kiin dl duo ro kit qud mdi. Vlic gldl cdc

bdl todn md sS phdt h-lin du^ ndng Ti/c gidi

todn cho HS.

Bdl vlit h-lnh bdy vl vi^ sdng tqo bdi todn

md thing quo dqy hqc hlnh hqc vi chO dl: Quan

h$ song song trong khdng gian d THPT. Khi dqy

hqc vi quan hi song song trong khdng glon, cd

Ihl xudt phdt K> bdl h3dn ddng dl phdt bllu ihdnh

bdi todn md. Xit cdc Hnh hudng sou ddy:

Bdl hdn ddng: Cho hlnh chdp S.ABCD cd

ddy Id hlnh thong, AD//BC. Gqi P, Q Idn luqt Id

h-qng tdm cda hal hm gldc SAB vd SCD; M, N

Idn luqt Id trung dilm cdo /\S vd CD. ChOng minh:

PQ//MH

Ody Id bdl todn ddng, yiu cdu ciJa bdi todn

duqc phdt bilu hrdng minh vd ngudt hqc di Hm

the^ Idi gidi. TO bdi todn ndy, to cd bdl todn md:

Bdl hdn md: Cho hlnh chdp S.y4BC0 cd ddy

Id hlnh thang, AD//BC. Gqi P, G Idn luqt Id frqng

ldm cOo hal tom gldc SAB vd SCD; M, N Idn luqt

HInhl

Id h-ung dilm cOa AB

vdCDihlnhl).

II Xdc d|nh v| tri

hjong ddl cOo MN vd

PQ. SO dvng kit qud

ndy, hdy: ojXdc djnh

v| tri tuong ddi cua

mdt sd' cdp dudng

thdng khdc; b) Chl ra

mdt sd' cdp (dudng

ihdng, m^t phdng) thdo mdn dudng thdng song

song vdi mdt phdng; c) Xdc djnh gioo hjy^ cOa

mdt ii cdp mdt phong; dIChJra Ong dvng hong

vlic Knh Hsddd ddl.

21 Nlu thoy ddl dliu klin cOo bdi hidn ddi

vdi cdc dilm P, Q hodc ddy cOa hlnh chdp Ihl cd

kit aud ndo? al Khdl qudt hda bdi k>dn; bl tX^

blit hdo bdl hxin; cj Cdc thoy ddi khdc ddl vdl

dliu klin vd kit qud.

Phdn Hch: ); HS cdn phdi dv dodn duqc

MN//PQ vd h, chOng minh.

Xit iSUN~=^~^^PQilMN. HS phdi

Hm ra nhOT>g Ong dvng cOo kit qud PQ//MN.

al VI MN Id dudng tnjng binh cOa hinh thong

ABCD nin MN//AD, MN//BC. TO MN//AD,

K)//MN => PQ//AD (kit qud 1); MN//BC,

PQ//MN => PQ//BC (kit qud 2).

b| VIPQ//MN. MNi^(ABa3l,PQ(t (ABCDj

nin PQ//IABa)l (kit qud 3); PQ//AD, AD c

(SAD), PQ <z (SADI => PQ//ISADI (kit qud 4);

PQ//BC, BCalSBCI, PQ<tlSBCI=> PQ///SBO

(kit qud 51; BC//PQ, BC<z lAPQI => BC//IAPQI

(kit qud d); AD//PQ, AD e IBPQI =» AD//IBPQI

(kit qud 7); MN//PQ, MN « lAPQ) => MN//

(APQI (kit qud 8); MN//PQ, MN rt (BPQI =>

MN//IBPQimqu6 9).

cl VI PQ//AD nen PQ e (PAD) =>

* TnMI nrr Ctqita B)i Iwc s< PM I U Il4i

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