7/31/2019 Chuyn 17. S dng phng php ta gii bi ton HH khng gian

1/3

Chuyen e 17: S DUNG PHNG PHAP TOA OGIAI TOAN HNH KHONG GIAN

PHNG PHAP:Bc 1:Chon he truc toa o Oxyz thch hp (chu y en v tr cua goc O)Bc 2:Xac nh toa o cac iem co lien quan

(co the xac nh toa o tat ca cac iem hoac mot so iem can thiet)Khi xac nh toa o cac iem ta co the da vao :

Y ngha hnh hoc cua toa o iem (khi cac iem nam tren cac truc totoa o).

Da vao cac quan he hnh hoc nh bang nhau, vuong goc, song song ,cuthang hang, iem chia oan thang e tm toa o

Xem iem can tm la giao iem cua ng thang, mat phang. Da vao cac quan he ve goc cua ng thang, mat phang.

Bc 3:S dung cac kien thc ve toa o e giai quyet bai toanCac dang toan thng gap:

o dai oan thang Khoang cach t iem en mat phang Khoang cach t iem en ng thang Khoang cach gia hai ng thang Goc gia hai ng thang Goc gia ng thang va mat phang Goc gia hai mat phang The tch khoi a dien Dien tch thiet dien Chng minh cac quan he song song , vuong goc Bai toan cc tr, quy tchBo sung kien thc :

1) Neu mot tam giac co dien tch S th hnh chieu cua no co dien tch S' bang tch cua S vi cosin cgoc gia mat phang cua tam giac va mat phang chieu

cos.' S S =2) Cho khoi chop S.ABC. Tren ba ng thang SA, SB, SC lay ba iem A', B', C' khac vi S

Ta luon co:

SC

SC

SB

SB

SA

SA

V

V

ABC S

C B AS '''

.

'''. ..=

MOT SO V DU MINH HOABai 1:Cho hnh chop SABC co ay ABCD la hnh vuong canh bang a, SA=3a va vuong goc vay

1) Tnh khoang cach t A en mat phang (SBC).2) Tnh khoang cach t tam O hnh vuong ABCD en mat phang (SBC).3) Tnh khoang cach t trong tam cua tam giac SAB en mat phang (SAC

Bai 2:Cho hnh chop SABCD co ay ABCD la hnh vuong tam O canh bang a, SO vuo

138

7/31/2019 Chuyn 17. S dng phng php ta gii bi ton HH khng gian

2/3

ay.Goi M,N theo th t la trung iem SA va BC. Biet rang goc gia MN va0 1) Tnh MN va SO.2) Tnh goc gia MN va mat phang (SBD) .

Bai 3: Cho hnh thoi ABCD tam O, canh bang a va AC=a, T trung iem H cua canh ASH(ABCD) vi SH=a

1) Tnh khoang cach t O en mat phang (SCD).2) Tnh khoang cach t A en mat phang (SBC).

Bai 4:Cho goc tam dien Oxyz, tren Ox, Oy, Oz lay cac iem A,B,C1) Hay tnh khoang cach t O en mat phang (ABC) theo OA=a, OB=b, OC=c2) Gia s A co nh con B, C thay oi nhng luon thoa man OA=OB+OC . H

tr cua B va C sao cho the tch t dien OABC la ln nhat.Bai 5:Cho t dien OABC (vuong tai O), biet rang OA,OB,OC lan lt hp vi mat p

goc ,, . Chng minh rang:1) 2coscoscos 222 =++ 2) 2222 ABC OCAOBC OAB S S S S =++

Bai 6:Cho hnh chop SABCD co ay ABCD la hnh vuong canh bang a, sa vuong goM,N la hai iem theo th t thuoc BC,DC sao cho

4

3,

2

a DN

a BM == . CMR hai mat phang

(SAM) va (SMN) vuong goc vi nhau.Bai 7:Cho tam giac eu ABC canh a. Goi D la iem oi xng vi A qua BC. Tren

goc vi mat phang (ABC) tai D lay iem S sao cho2

6aSD = , CMR hai mat phang (SAB) v

(SAC) vuong goc vi nhau. Bai 8:Trong khong gian cho cac iem A,B,C theo th t thuoc cac tia Ox, Oy, Oz vuon

tng oi mot sao cho OA=a , OB=2a . OC=c (a,c>0). Goi D la iem oi dien vi O c

ch nhat AOBD va M la trung iem cua oan BC. (P) la mat phang qua A,M v(OCD) theo mot ng thang vuong goc vi AM.a) Goi E la giao iem cua (P) vi OC , tnh o dai oan OE.b) Tnh t so the tch cua hai khoi a dien c tao thanh khi cat khoi chop

mat phang (P).c) Tnh khoang cach t C en mat phang (P).

Bai 9:Cho t dien SABC co SC=CA=AB=2a , )( ABC SC , ABC vuong tai A, cac iem Mthuoc SA va N thuoc BC sao cho AM=CN=t (0

7/31/2019 Chuyn 17. S dng phng php ta gii bi ton HH khng gian

3/3

2) Goi M la iem chia oan AD theo ty so 3= MD

AM . Hay tnh khoang cach t M en

phang (AB'C).3) Tnh the tch t dien AB'D'C.

Bai 13: Cho hnh lap phng ABCD.A'B'C'D' canh bang a..Goi M, N la trung iem cua BC va'1) CMR .)( '' BD A AC

2) CMR .) //(' BD A MN

3) Tnh khoang cach gia BD na MN theo aBai 14:Cho lang tru ABCD.A'B'C'D' co ay ABCD la hnh thoi tam O canh bang a, goc A=0 . B'O

vuong goc vi ay ABCD, cho BB'=a1) Tnh goc gia canh ben va ay.2) Tnh khoang cach t B, B' en mat phang (ACD').

Bai 15:Cho hnh vuong ABCD canh bang a tam I . Tren hai tia Ax, By cung chieu va goc vi mat phang (ABCD) lan lt lay hai iem M,N . at AM=x, CN=y

1) Tnh the tch hnh chop ABCMN.2) CMR ieu kien can va u e goc MIN=900 la 2xy=a2 .

Bai 16: Cho hnh chop S.ABC co ay la tam giac vuong can ABC vi canh huyen A2Canh ben va SC = 2 .Goi M la trung iem cua AC, N la trung iemSC (ABC)

1) Tnh goc cua hai ng thang SM va CN2) Tnh o dai oan vuong goc chung cua SM va CN.

Bai 17: Cho hnh lap phng ABCD.A'B'C'D' co canh bang 11) Goi M, N lan lt la trung iem cua AD, BB' .Chng minh rang .'A C MN

Tnh o dai oan MN2) Goi P la tam cua mat CDD'C' . Tnh dien tch .MNP

Bai 18: Cho hnh chop S.ABCD co ay ABC la tam giac eu canh a va canh ben SA

mat phang ay (ABC) . Tnh khoang cach t iem A ti mat phang (SBC) tSA=a 6

2Bai 19: Cho t dien OABC co ba canh OA;OB;OC oi mot vuong goc . Goi lan; ;

gia mat phang (ABC) vi cac mat phang (OBC);(OCA) va (OAB).Chng micos cos cos 3 + +

Bai 20: Cho hnh chop S.ABCD co ay ABCD la hnh vuong canh a , SA vuong goc v(ABCD) va SA=a . Goi E la trung iem cua canh CD . Tnh theo a khoang cach ng thang BE.

Bai 21: Cho lang tru ng ABC.A'B'C' co ay ABC la tam giac can vi AB=AC=a vaBAC = 1200, canh ben BB' = a. Goi I la trung iem CC'. Chng minh rang tam giavuong A. Tnh cosin cua goc gia hai mat phang (ABC) va (AB'I).

-------------Het----------

140