HÌNH HỌC 11 HAY NHẤT

Bp GIAO DUC VA DAO TAO HINH HOC /3); (C) 341 + >/3); (D) Khdng tfnh duge Cho hinh binh hdnh ABCD Ggi Bx, Cy, Dz Id edc dudng thing song song vdi ldn Iugt di qua B, C, D vd nam vl mdt phfa eua mat phlng {ABCD), ddng thdi khdng nim mdt phlng (ABCD) Mdt mat phang di qua A vd clt Bx, Cy, Dz ldn Iugt tai B', C^D' vdi BB' = 2, DD' = Khi dd CC bing (A)3; (B)4; (C) ; (D) 10 Tim mdnh dl dflng cdc menh dl sau : (A) Hai dudng thing phdn biet cflng nim mdt mat phlng thi khdng cheo nhau; (B) Hai dudng thing phdn biet khdng cat thi cheo ; (C) Hai dudng thing phdn biet khdng song song thi cheo ; (D) Hai dudng thing phdn biet ldn Iugt thude hai mat phlng khae thi cheo 11 Cho hinh vudng ABCD vk tam giac diu SAB nim hai mat phlng khdc Goi M la dilm di ddng trdn doan AB Qua M ve mdt phang (or) song song vdi (SBC) Thie't dien tao bdi (a) vk hinh chop SABCD Id hinh gi ? (A) Tam giac; (B) Hinh binh hdnh ; (C) Hinh thang ; (D) Hinh vudng 12 Vdi gia thie't cua bdi tap 11, ggi A^, F, Q ldn Iugt la giao cua mat phlng {d) vdi cae dudng thing CD, DS, SA Tdp hgp cdc giao dilm / cfla hai dudng thing MQ vk NPlk (A) Dudng thing ; (B) Nfla dudng thing ; (C) Doan thing song song vdi AB; (D) Tdp hgp rdng 80 ^ Ta-le! nguoi dau tien phat hien nhat thuc Mgi ngudi chflng ta diu bilt dlh dinh If Ta-let hinh hgc phlng vd trOng hinh hgc khdng gian Ta-let la mdt thuang gia, mdt ngudi thfch di du Iich vd mdt nhd thidn vdn kiem trilt hgc Ong Id mdt nhd bdc hgc thdi cd Hi Lap vd la ngudi sdng ldp trudng phdi trilt hgc tu nhien d Mi-let Ong cung duge xem Id thuy t6 cua bd mdn Hmh hgc Trong Iich sfl bd mdn Thidn vdn, Ta-ldt Id ngudi ddu tien phdt hien nhdt thue vdo ngdy 25 thdng nam 585 trudc Cdng nguydn 6ng da khuyen nhihig ngudi di biln xdc dinh phuong hudng bdng cdch dua vdo chdm Tilu Hflng Tinh dQcth^ QiCfi thieu phuang phap tien de viec xay dung hinh hoc Trong luc cfiuyen tro, Hin-be (Hilbert) noi dua rdng "Trong hint) tioc, ttiay cho diSm, dudng thdng, mdt phdng ta co the noi ve cai ban, cai ghe vd nhung cdc bia." Tfl the' ki thfl ba trudc Cdng nguydn, qua tac phdm "Co ban", 0-elft la ngudi ddu tien ddt nIn mdng cho vide dp dung phuang phdp tien dl viec xdy dung hinh hgc Y tudng tuyet vdi eua 0-elft da duge hodn thidn bdi nhilu the' he todn hgc tilp theo vd mai dlh cud'i the' ki XDC, Hin-be, nhd todn hgc Dflc, tac phdm "Co sd hinh hgc" xudt ban ndm 1899 da dua mdt he tien dl ngln, ggn, ddy dfl vd khdng mdu thudn Ngdy cd nhilu tac gia khae dua nhitng he tien dl mdi eua hinh hgc 0-elft nhung vl eo ban vdn dua vdo he tidn dl Hin-be Sau ddy chflng ta se tim hiiu so luge vl phuong phdp tien dl 6-HiNH HOC 11-A 81 l.Tiindeldgi? Trong sdch giao khoa hinh hgc b hudng phd thdng, chflng ta da gap nhflng khdi niem ddu tien cua hinh hgc nhu dilm, dudng thing, mat phlng, dilm thude dudng thing, dilm thude mat phlng.v.v Cdc khai nidm ndy dugc md ta bing hinh anh eua chung vd diu khdng dugc dinh nghia Ngudi ta ggi dd la cdc khdi niim ca bdn vk dflng chung dl dinh nghia edc khdi nidm khdc Hon nfla, hgc Hinh hgc, chflng ta cdn gap nhiing mdnh dl todn hgc thfla nhdn nhung tfnh chdt dflng din don gian nhdt cua dudng thing vd mat phlng ma khdng ehiing muih, dd la cae tiin de hinh hgc Thf du nhu: - Cd mdt vd chi mdt dudng thing di qua hai dilm phdn bidt cho trudc ; - Cd mdt vd chi mdt mdt phlng qua ba dilm khdng thing hdng cho trudc ; - Ndu cd mdt dudng thing di qua hai dilm cua mdt mat phlng thi mgi dilm cua dudng thing diu thude mat phlng dd ; V V Ngudi ta dua vdo cdc tidn dl Hinh hgc dl chiing minh cdc dinh If cua Hiiih hgc vd xdy dung toan bd ndi dung cua nd Mdt hd tien dl hoan chinh phai thoa man mdt sd dilu kidn sau : - He tien dl phai khdng mdu thudn ; - Mdi tidn dl cfla he phai ddc ldp vdi cdc tidn dl cdn lai; - He tien dl phai ddy dfl Cdc li thuyet hinh hgc Chflng ta bie't ring mdi If thuylt hinh hgc ed mdt he tien dl rieng cfla nd Ridng hinh hgc 0-clft vd hinh hgc Ld-ba-sep-xki chi khdc vl tidn dl song song, edn tdt ca edc tidn dl edn lai cua hai H thuylt hinh hgc ndy diu gidng Trong sach gido khoa Hinh hgc ldp 7, tidn dl 0-elft vl dudng thing song song dugc phdt bilu nhu sau : M d "Qua mdt diim M ndm ngodi mdt dudng thdng a chi cd mdt dudng thdng d song song vdi dudng thdng a " Trong edc gido tiinh vl co sd hinh hgc, tien dl ndy dugc ggi la tidn d6 V efla 0-clft Sudt han 2000 nam ngudi ta da nghi 82 6-HlNH Hex 11-B ngd cho ring tien dl V Id mdt dinh h ehfl khdng phai la mdt tidn dl vd tim cdch chflng mmh tien dl V tfl cdc tien dl cdn lai, nhung tdt ca diu khdng di ddn ke't qua Tien dl V cdn dugc phdt bilu mdt each ehfnh xdc nhu sau: "Trong mat phang xde dinh bdi dudng thing a vd mdt dilm M khdng thude a cd nhilu nhd't Id mdt dudng thing di qua dilm M va khdng eat a" Sau dd ngudi ta ddt tdn cho dudng thing khdng cat a ndi trdn la dudng thing song song vdi a Ld-ba-sep-xki la ngudi ddu tidn dat v& dl thay tien dl 0-clft bing tien dl Ld-ba-sep-xki nhu sau: 'Trong mat phdng xdc dinh bdi dudng thdng a vd mdt diim M khdng thude a cd it nhdt hai dudng thdng di qua M vd khdng cdt a " Tfl tidn dl ngudi ta chiing minh duge tdng eae gdc mdi tam gidc diu nho hon hai vudng vd xdy dung ndn mdt mdn Hinh hgc mdi la Hinh hgc Ld-ba-sip-xki Ngdy nay, Hinh hgc Ld-ba-sep-xki ed nhilu flng dung nganh Vdt If vu tru vd da tao ndn mdt bude ngoat vide lam thay ddi tu khoa hgc cua ngudi 83