"Thiết Kế Bài Giảng Hình Học 12 Tập 1
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TRAN VIN H
I hiet ke bai giang HlNH HQC]TAP MOT
NHA XUA T BAN H A N6 I
TRAN VINH
THIET KE BAI GIANG HINH HOC 12 TAPMOT
NHA XUAT BAN HA NOI
LCll NOI DAU
Chifcfng trinh thay sach gan lien vdi viec do! moi phiidng phap day hoc, trong do c6 viec thifc hien ddi mcfi pbifdng phap day hoc trong mon Toan. Bo sach Thiei kebdi gidng Hinh hpc 12 ra dcrt de phuc vu viec ddi mcfi do.
Bp sacb difdc bien scan difa tren cac chifcfng, muc cua bo sach giao khoa (SGK), bam sat noi dung SGK, tii do hinh thanh nen cau tnic mot bai giang theo chifcfng trinh mdi difcfc viet theo quan diem boat dong va muc tieu giang day la: Lay hoc sinh lam trung tam va tich cifc suf dung cac phifcfng tien day hoc hien dai.
Phan Hinh hoc gom 2 tap.
Tap 1: gom cac chifcfng I va mot phan chifcfng II
Tdp 2 : gom phan con lai cua Chifcfng II va chifcfng III
Trong moi bai scan, tac gia co 6\ia ra cac cau hoi va tinh hudng thu vj. Ve boat dong day va hoc, chiing toi cd gang chia lam 2 phan: Phan boat dong cua giao viSn (GV) va pban boat dong cua hoc sinh (HS), cf moi phan c6 cac cau hoi chi tiet va hifcfng dan tra ldi. Thifc hien xong moi boat dong, la da thifc hien xong mpt dcfn vi kien thufc hoac cung cd dcfn vi kie'n thifc do. Sau m6i bai hpc chiing toi CO difa vac phan cau hoi trac nghiem khach quan nham de hpc sinh tif danh gia difcfc miifc dp nhan thifc va mifc dp tiep thu kien thufc cua minh. Phan hinh ve, cac tac gia cd gang sifu tam nhifng hinh anh thifc te co gan lien vdi lich suf toan hpc trong chifcfng trinh Hinh hpc 12 nhif cac hinh da dien deu, ...Day la nhuhg hinh ma khi iing dung trong bai giang se gay nhieu hiing thii trong hpc tap cua hpc sinh.
Day la bp sach bay, dufcfc tap the tac gia bien soan cong phu, lihg dung mpt sd thanh tifU khoa hpc nhat dinb trong tinh toan va day hpc. Chiing toi hy vpng dap ufng difcfc nhu cau cua giao vi6n toan trong viec ddi mdi phifcfng phap day hpc.
Trong qua trinb bien soan, khong the tranh khoi nhOhg sai sot, mong ban dpc ram thong va chia se. Chiing toi chan thanh cam cfn sif gop y cua cac ban.
Hd Noi thdng 7 ndm 2008
Tac gia
ChirONq 1
KHOI DA mix
Phan 1
Gidl THltu CHLfdNG
I. CAU TAO CHUDNG
§1. Khdi niem \6 khdi da didn
§2 Khdi da dien Idi va khdi da dien deu
§3. Khai nidm ve the tich khdi da dien
On tap chuong I
Muc dich cua chuong
• Chuong I nham cung ca'p cho hoc sinh nhCing kie'n thiic co ban v6 khai niem cac khdi da di6n trong kh6ng gian, chu yeu la cac da dien Idi:
Khdi da dien, khdi chop.
Khai ni6m ve hinh da dien, khdi da dien.
Hai da dien bang nhau la gi ?
- Cac chia va ghep cac khdi da dien.
• Gidi thi6u ve khdi da di6n ldi va khdi da di6n deu.
• The tfch ciia khdi da dien:
Khai niem v^ th^ tfch khdi da dien.
Khai ni6m va cong thiJc th^ tfch khdi da dien.
The tfch khdi lang tru.
Thi tfch khdi chop.
II- MUC TIEU
1. Kie'n thurc
Nam duoc toan bo kie'n thiic co ban trong chuong da neu tren.
Hieu cac khai niem va tfnh chat ciia khdi da dien.
" Hieu ve each thiic xay dung the tfch mot sd khdi da dien.
Hi6u dugc khdi da dien ldi.
2. KT nang
Phan biet dugc khdi da dien.
Tfnh dugc the tfch cua hinh lang tru, hinh chdp.
- Chiing minh dugc hai mat phang vuong gdc.
3. Thai do
Hgc xong chuong nay hgc sinh se lien he dugc vdi nhi6u va'n de thuc te sinh dgng, lien he dugc vdi nhiing van de hinh hgc da hgc b Idp dudi, md ra mgt each nhin mdi ve hinh hgc. Tix 66, cac em cd the tu minh sang tao ra nhiing bai toan hoac nhirng dang toan mdi.
Ke't ludn
Khi hgc xong chuong nay hgc sinh can lam tdt cac bai tap trong sach giao khoa va lam dugc cac bai kiem tra trong chuong.
Pha u 2>
ckc BAI SOAN
§1. Khai niem khoi da dien
(tiet 1, 2, 3)
I. MUC Tif U
1. Kien thurc
HS nam dugc:
1. Khai niem khdi da di6n trong khdng gian.
2. Hi^u va van dung tinh th^ tich khdi lang tru va khdi chop.
3. Khai niem \i hinh da di6n \h. khdi da di^a
2. Kl ndng
• Ve thanh thao cac khdi da difin don gian.
• van dung thanh thao mdt sd phep bi6i hinh : Ddi xumg tam, ddi xiing true. • Phan chia va ghep thanh thao khdi da didn.
3. Th^i do
• Lien h6 dugc vdi nhi^u vah 6i thuc te trong khdng gian.
• Cd nhi^u sang tao trong hinh hgc.
• Humg thu trong hgc tap, tfch cue phat huy tfnh ddc lap trong hgc tap.
n. CHUAN BI CUA GV VA H&
1. Chu^nbicua GV:
• Hinh ve 1.1 d^n 1.14.
• Thudc ke, pha'n mau,...
2. Chuan bj cua HS :
Dgc bai trudc d nha, cd the lien he cac phep bien hinh da hgc d ldp dudi. in. PHAN PHOI THC5I LUONG
Bdi dugc chia thdnh 3 tie't:
Tie't 1: Tir dau de'n bet muc 1 phan II.
Tie't 2: Tie'p theo de'n bet phan III
Tie't 3: Tie'p theo den bet phan IV va phan bai tap
IV. TIEN TBlNH DAY HOC
n. f>^J VAN DC
Cau hdi 1.
Nhac lai khai niem hinh hop, hinh chdp.
Cau hoi 2.
Cho hinh hop ABCDA'B c u
a) Hay xac dinh cac mat cua hinh hop.
b) Hay xac dinh cac dinh va cac canh ciia hinh hop.
a. RM MOI
• Thuc hien A l trong 5 phiit.
Hoat dgng cua GV
Cdu hoi I
Nhac lai dinh nghia hinh lang tru. Neu mgt sd vf du.
Cdu hoi 2
Nhac lai dinh nghla hinh chdp. Neu mgt sd vi du.
Hoat dgng ciia HS
Ggi y trd loi cdu hoi I HS tu neu.
Ggi ytrd loi cdu hoi 2 HS tu neu.
HOATDONCI
I. KH6 I LANG TRU VA KH6 I CHOP
GV neu cau hoi :
HI. Khdi rubic cd bao nhieu mat?
H2. Mdi mat ciia khdi rubic la hinh gi?
• GV six dung hinh 1.2 trong SGK va dat van d6:
H3. Hay dgc ten cac khdi chdp d hinh 1.2.
H4. Hay ke ten cac mat cua hinh 1.2.
H5. Hay ke ten cac mat day cua hinh 1.2
H6. Cac canh ben ciia hinh lang tru cd quan h6 vdi nhau nhu the nao? H7. Neu mgt sd hinh anh thuc te ve hinh lang tru va hinh chdp.
nOATDONG2
n. KHAI NifiM Wt HINH DA DifiN VA KHOI DA DI£ N
1. Khai niem ve hinh da di^n
Stt dung hinh 1.4
• Thuc hien A 2 trong 4 phut.
Hoat dong ciia GV
Cdu hoi I
Hay ke ten mat day ciia hinh lang tm ABCDE.A'B'C'D'E'
Cdu hoi 2
Hay k^ ten mat day ciia hinh chdp S.ABCDE.
Hoat dpng cua HS
Ggi y trd l&i cdu hoi I Do la cac hinh da giac ABODE va A'B'C'D'E' Ggi y trd loi cdu hoi 2 Do la hinh da giac ABODE.
• GV dat cac cau hoi sau :
H8. Trong hinh 1.4 hinh lang tru cd nhOng da giac nao?
H9. Trong hinh 1.4 hinh chdp cd nhung da giac nao?
HIO. Cac da giac cua cac hinh tren quan he vdi nhau nhu the nao? • GV neu tfnh chat:
a) Hai da gidc phdn biet chi cd the : Hoac khdng cd diem chung hoac cd mdt cgnh chung.
b) Mdi cgnh ciia da gidc ndo cUng Id cgnh chung cOa dUng hai da gidc. • GV n6u dinh nghia hinh da dien:
Hinh da dien Id hinh dugc tgo bdi cdc da gidc thda mdn 2 tinh chdt tren. Hll. Hay ndu mdt sd vf du v^ hinh da didn.
HI2. Hay k^ ten hinh da diSn cd cac da giac bang nhau.
H14. Trong hinh 1.5 em hay k^ tdn cac day ciia hinh da didn.
2. Khai niem ve khdi da di^n
• GV ndu dinh nghla :
Khdi da dien Id phdn khdng gian dugc gidi hgn bdi hinh da dien, ke cd hinh da dien dd.
• GV cd th^ lay mdt hinh da didn, bo bdt di mdt sd mat va hoi:
H15. Hinh viia nhan dugc cd phai khdi da didn hay khdng?
• GV ndu cac khai nidm :
HI6. Di^m trong ciia khdi da didn la gi?
HI7. Di^m ngoai cua khdi da didn la gi?
H18. Cd di^m nao khdng la di^m trong cung khdng la di^m ngoai ciia khdi da didn. H19. Mi6n trong ciia khdi da didn la gi?
H20. Mien ngoai ciia khdi da didn la gi?
H21 .Mdt dudng thang cd th^ nam trgn d mi^n nao ciia khdi da didn? H22. Hay ke tdn mdt sd hinh khdng phai la khdi da didn.
10
• Thuc hidn ^ 3 trong 4 phiit.
Hoat dgng ciia GV
Cdu hoi I
Hinh 1.8c cd vi pham tfnh chat nao khdng ?
Cdu hoi 2
Giai thfch vi sao hinh 18c khdng phai la khdi da dien
Hoat ddng ciia HS
Ggi y trd loi cdu hoi I
Vi pham tfnh chat a.
ABODE va A'B'C'D'E'
Ggi y trd led cdu hoi 2
GV cho HS phat bi^u va kdt luAn.
HOATDONC 3
HL HAI DA DifeN BANG NHAU
1. Phep ddi hinh trong khong gian
• GV ndu dinh nghia:
Trong khdng gian, quy tdc dgt tuang Ang mdi diem M vdi duy nhdt mat diem M' dugc ggi Id phep bie'n hinh trong khdng gian.
Phep bien hinh trong khdng gian la phep ddi hinh neu nd bdo todn khodng cdch.
• GV ndu mdt sd phep ddi hinh thudng gap trong khdng gian.
a) Phep tinh tien theo vecta v
Phep tinh tien theo vecta v Id phep bien hinh bien M thdnh M' md MM' = v
H22. Hay chiing minh phep tinh tien theo vecto v la phep ddi hinh. b) Phep ddi xicng qua mat phdng (P)
• GV sit dung hinh 1.10b va ndu khai nidm:
11
Phep dd'i xiing qua mat phdng (P) la phep bien hinh bie'n mdi diem thudc (P) thdnh chinh nd. Bie'n mdi diem M khdng thugc (P) thdnh M' md (P) la mat phdng trung trUc ciia MM'.
H23. Hay chiing minh phep ddi xiing qua mat phang (P) la phep ddi hinh. c) Phep ddi xdng tdm O
GV sit dung hinh 1.1 la va ndu khai niem:
Phep ddi xdng tdm O la phep biin hinh bie'n O thdnh chinh nd. Bien mdi diem M khdc O thdnh M' md O la trung diem cua MM'
H24. Hay chiing minh phep ddi xiing tam O la phep ddi hinh.
d) Phep ddi xiing qua dudng thdng A
GV sii dung hinh 1.1 la va neu khai niem:
Phep dd'i xdng qua dudng thdng A la phep bien hinh bien mdi diem thudc A thdnh chinh nd. Biin mdi diem M khdng thudc A thdnh diem M' md A la dudng trung true cua MM'.
H25. Hay chung minh phep ddi xiing qua dudng thang A la phep ddi hinh. • GV neu nhan xet:
Thuc hien lien tie'p cdc phep ddi hinh ta dugc phep ddi hinh.
Phep ddi hinh biin da dien (H) thdnh da dien (H') vd dinh, cgnh, mat cua (H) thdnh dinh, cgnh, mat cua (H').
2. Hai hinh bang nhau
• GV ndu dinh nghla:
Hai hinh dugc ggi Id bdng nhau neu nd cd mdt phep ddi hinh bie'n hinh ndy thdnh hinh kia.
GV su dung hinh 1.12 de md ta dinh nghia tren.
• Thuc hien A 4 trong 4 phiit.
12
B'
A'
Hoat dgng ciia GV
Cdu hoi I
Ggi 0 la tam cua hinh hop. Phep ddi xiing tam 0 bien hinh lang tru ABD.A'B'D' thanh hinh nao ?
Cdu hoi 2
Chiing minh hai hinh hop tren bang nhau.
Cdu hoi 3
Hay tim mgt phep bie'n hinh khac bie'n ABD.A'B'D thanh hinh CDB.C'B'D'
Hoat dgng ciia HS
Ggi y trd ldi cdu hoi I
ABD.A'B'D' thanh hinh CDB.C'B'D'
Ggi y trd ldi cdu hoi 2
HS tu chiing minh.
Ggi y trd ldi cdu hoi 3
HS tu tim.
nOATDONG 4
IV. PHAN CHIA VA LAP GHEP CAC KHOI DA DI£ N
• GV neu each chia mdt sd khdi da dien va dat cau hdi:
H26. Khi nao cd the chia mgt khdi da dien thanh hai khdi da dien khac nhau? H27. Hinh hop chii nhat cd the chia dugc thanh hai khdi da dien hay khdng? hay neu each chia va ke ten cac khdi da dien tao thanh.
• GV neu nhan xet:
Mdt khdi da didn bat ki cd the chia thanh cac khdi da dien.
13
HOATDONG^
TbM TflT Bfll HQC
1. a) Hai da giac phan bidt chi cd th^ : Hoac khdng cd diem chung hoac cd mdt canh chung.
b) Mdi canh ciia da giac nao ciing la canh chung ciia diing hai da giac. 2. Hinh da didn la hinh dugc tao bdi cac da giac thda man 2 tfnh cha't trdn.
Khdi da didn la ph^ khdng gian dugc gidi han bdi hinh da didn, ke ca hinh da didn dd.
3. Trong khdng gian, quy tac dat tuong iing mdi didm M vdi duy nha't mdt diem M' dugc ggi la phep bid'n hinh trong khdng gian.
Phep bie'n hinh trong khdng gian la phep ddi hinh neu nd bao toan khoang each.
4. Phep tinh tid'n theo vecto v la phep bie'n hinh bid'n M thanh M' ma MM' = v. 5. Phep ddi xumg tam O la phep bid'n hinh bid'n O thanh chfnh nd. Bid'n mdi diem M khac O thanh M' ma O la trung diem ciia MM'
6. Ph6p ddi xumg qua dudng thang A la phep bid'n hinh bidn mdi diem thudc A thanh chfnh nd. Bidn mdi didm M khdng thudc A thanh diem M' ma A la dudng trung true ciia MM'
7. Thuc hidn lidn tidp cac phep ddi hinh ta dugc phep ddi hinh.
Phep ddi hinh bien da didn (H) thanh da didn (H') va dinh, canh, mat cua (H) thanh dinh, canh, mat ciia (H').
8. Hai hinh dugc ggi la bang nhau nd'u nd cd mdt phep ddi hinh bidn hinh nay thanh hinh kia.
14
HOATDQNG 6
MOT S6 CflU H6 | TRflC NGHIpM
Hay dien diing (D) sai (S) vao cac khang dinh sau :
Cdul. Cho hmh hdp ABCDEFGH
B
(a) Hinh hop trdn la mdt khdi da didn
(b) Cd the chia hinh hop trdn thanh hai lang tru bang nhau (c) Tdn tai phep ddi xiing tam O bid'n cac dinh cua hinh hop thanh cac dinh ciia nd
(d) Ca ba khang dinh trdn ddu sai
Trd ldi.
D •
D D
a
D
b D
c
D
d S
Cdu 2. Cho hinh hdp ABCD.A'B'CD'. Ggi O la tam ciia hinh hdp, phep ddi xiing tam D(o)
15
B' C
A' y^ 1 "•
B: .-' \
**• • .
(a)D(0)(A) = C'
(b)D(0)(B) = B'
(c)D(0)(B)-D'
(d)D(0)(A) = C.
Trd ldi.
^.^^
D'
D
D
1
D
D
a D
b S
c
D
d S
Cdu 3. Cho hinh hop ABCD.A'B'CD'. Ggi O la tam ciia hinh hop, phep ddi xiing
tam D, '(O)
B'
f j r
A' y 1 N
1 ^ ^'' '
D'
B
yy \- - y^'
(a) D(0)(BAC.B'A'C') = DAC.D'A'C' (b) D(0)(ABD.A'B'D') = CBD.C'B'D'
D D
(c) D(0)(ABCD.A'B'C'D') = ABCD.A'B'C'D' (d) Ca ba khang dinh tren deu sai.
16
D D
Trd ldi.
a D
b D
c
D
d S
Cdu 4. Cho hinh chdp ddu S.ABCD (hinh ve)
A B
(a) Hai hinh chdp S.DOA va S.BOA bang nhau (b) Hai hinh chdp S.DOC va S.BOC bang nhau (c) Hai hinh chdp S.BOA va S.BOC bang nhau (d) Ca ba khang dinh tren deu sai
Trd ldi.
• • D D
a D
b D
c
D
d S
Chgn khang dinh diing trong cac cau sau:
Cdu 5. Cho hinh chdp deu S.ABCD (hinh ve). Qua phep ddi xiing qua mat phang (SDB) bie'n hinh chdp S.AOB thanh hinh chdp
17
(a) S.DOA ; (c) S.COB; Trd ldi. (c).
(b) S.DOC (d) S.DBC
Cdu 6. Cho hinh chdp deu S.ABCD (hinh ve). Qua phep ddi ximg qua mat phang (SDB) bie'n hinh chdp S.DAB thanh hinh chdp
(a) S.DOA ; (c) S.COB; Trdldi. (d).
18
(b) S.DOC (d) S.DBC
Cdu 7 Cho hinh chdp deu S.ABCD (hinh ve). Qua phep ddi xirng qua mat phang (SAC) bie'n hinh chdp S.DAB thanh hinh chop
(a) SDOA ; (b) S.DOC (c) S.COB i (d) S.DAB Trdldi. (d).
Cdu 8. Cho hinh chdp ddu S.ABCD (hinh ve). Qua phep ddi xiing qua mat phang (SAC) bie'n hinh chdp S.OAB thanh hinh chdp
(a) S.DOA; (c) SCOB; Trdldi. (a).
(b) S.DOC
(d) S.DAB
19
Cdu 9. Cho hinh chdp deu S.ABCD (hinh ve). Qua phep ddi xung tam O bie'n hinh chop S.OAB thanh hinh chdp
(a) S.DOA; s' (b) S.DOC (c) S.AOB ; (d) S.DOC Trd ldi. (d).
Cdu 10. Cho hinh chdp deu S.ABCD (hinh ve). Qua phep ddi xiing tam O bie'n hinh chdp S.ABCA thanh hinh chdp
20
(a) S.DOA ; (c) S.AOB; Trd ldi. (b).
(b) S'.ABCD
(d) S.DAB
HOATDQNG 7
HaOTNG DflN Bfll TflP SGK
Bai 1. Hudng ddn. Dua vao tinh chat ciia da dien
Hai mat kd nhau ludn cd mgt canh chung
Mdi canh cua da dien la canh chung cua hai mat.
Hoat dgng cua GV
Cdu hoi I
Gia sii da dien cd n mat, cac mat khdng cd canh chung thi cd tat ca bao nhieu canh ?
Cdu hoi 2
Mdi canh ciia da dien la canh chung ciia 2 mat nen sd mat la bao nhieu ?
Cdu hoi 3
Nhan xet vdsd mat.
Cdu hoi 4
Neu vf du.
Hoat dgng cua HS
Ggi y trd ldi cdu hoi I Cd tat ca 3n canh.
Ggi y trd ldi cdu hoi 2
Co tat ca — mat.
2 •
Ggi y trd ldi cdu hoi 3 Sd mat phai cbSn.
Ggi y trd ldi cdu hoi 4 HS tu lay vi du.
Bai 2. Hudng ddn. Dua vao tfnh chat ciia da dien
Dinh cd k mat di qua thi cd k canh di qua.
Mdi dinh cd it nhat la 3 mat di qua.
21
Hoat dgng cua GV
Cdu hoi 1
Mdi canh cua da dien di qua ma'y dinh.
Cdu hoi 2
Tdng sd canh so vdi tdng sd mat nhu the nao?
Cdu hoi 3
Sd mat di qua mgt dinh la chan hay le ?
Cdu hoi 4
Sd dinh la chan hay le?
Hoat dgng ciia HS
Ggi y trd ldi cdu hoi I
Mdi canh ciia tii dien di qua dung 2 dinh.
Ggi y trd ldi cdu hoi 2
Tdng sd canh bang 2 lan tdng sd mat.
Gai y trd ldi cdu hoi 3
La sd le.
Ggi y trd ldi cdu hoi 4
Sd dinh phai la so chan.
HS tu neu vf du.
Bai 3. Hifdng ddn. Dua vao tfnh cha't ciia da dien va hinh lap phuong. Hinh lap phuong cd 8 dinh va 6 mat.
Sd canh cua hinh lap phuong la 12.
G
Hoat dgng cua GV t
Cdu hoi I
Hay ke ten 5 hinh tii dien d hinh tren.
Cdu hoi 2
Cdn each chia nao khac khdng? Cdu hoi 3
Hay neu mgt each chia khac.
22
Hoat dgng cua HS
Gg-' y trd ldi cdu hoi I
HS tu tra Idi.
Ggi y trd ldi cdu hoi 2
van cdn nhidu each chia khac niia. Ggi y trd ldi cdu hoi 3
HS tur tra ldi
Bai 4. Hudng ddn. Dua vao tfnh chat ciia da dien va hinh lap phuong. Hinh lap phuang cd 8 dinh va 6 mat.
Sd canh ciia hinh lap phuong la 12.
F • G -
/
H
D
Hoat dgng ciia GV
/'j\
D^l-. B ^ /V^ ' /-•
y s
A
Hoat dgng cua HS
Cdu hdi I
Hay kd ten 6 hinh tii dien d hinh tren.
Cdu hoi 2
Cdn each chia nao khac khdng? Cdu hoi 3
Hay neu mdt each chia khac.
Ggi y trd ldi cdu hoi I
HS tu tra ldi.
Ggi y trd ldi cdu hoi 2
Van cdn nhidu each chia khac niia Ggi y trd ldi cdu hoi 3
HS tu neu.
23
§2. Khoi da dien loi va khoi da dien deu (tiet 4, 5)
I. MUC TIEU
1. Kie'n thurc
HS nam dugc:
1. Dinh nghia khdi da dien ldi, phan biet dugc khdi da dien loi va khdi da dien deu. 2. Nam dugc dinh nghia khdi da dien ddu.
3. Hieu rd tfnh chat ciia khdi da dien deu.
4. Nhan bie't dugc mdt so khdi da dien ddu.
2. KT nang
• Bie't phan biet da dien ldi va da dien khdng ldi.
• Bie't dugc mgt sd da dien ddu va chiing minh dugc mdt da dien la d:i dien ddu. 3. Thai do
Lien he dugc vdi nhidu van dd cd trong thuc te vd hai dudng thang vudng gdc. Cd nhidu sang tao trong hinh hgc.
Hiing thii trong hgc tap, tich cue phat huy tfnh ddc lap trong hgc tap.
II. CHUAN 51 CUA GV VA HS
1. Chuan bi ciia GV:
• Hinh ve 1.17 den 1.22 trong SGK.
• Thudc ke, pha'n mau,...
• Chuan bi san mgt vai hinh anh thuc te trong trudng vd hai dudng thang vudng gdc nhu: cac dudng thang cua tudng,...
2. Chuan bj ciia HS :
• Dgc bai trudc d nha, dn tap lai mdt sd tfnh cha't hinh chdp va hinh tru. • Chudn bi thudc ke, biit chi, biit mau dd ve hinh.
24
in. PHAN PHOI TH6I LUONG
Bai nay chia thanh 2 tiet:
Tie't 1: Tit dau de'n bet dinh nghia phan II.
Tiet 2 : Phan cdn lai va hudng dan bai tap.
IV. TIEN TDINH DAY HOC
n. DRT Vn'N D€
Cau hoi 1.
Cho hinh chdp S.ABCD. Day la hinh vudng.
a) Ne'u SA vudng gdc vdi day thi cac mat ben cd quan he nhu te' nao? b) SA vudng gdc vdi day nhung day ABCD la hinh binh hanh thi cac mat ben cd quan he nhu the nao?
Cau hoi 2.
Neu mdt sd tfnh cha't co ban ciia hinh da dien.
a. am AA6I
HOATDQNGl
I. KHOI DA DifeN LOI
GV sit dung hinh 1.17 (nen dat ten cac dinh va cac diem) va neu van dd : 25
a) ^ b)
HI. Em cd nhan xet gi vd doan thang EF trong hinh a)?
H2. Em cd nhan xet gi vd doan thang MN trong hinh b)?
GV nen lay mdt khdi da didn khdng Idi de so sanh.
Tren hinh ve M e mp(EFF'E), N e mp(DEE'D').
H3. MN cd nam trgn trong hinh lang tru dd khdng?
• GV neu dinh nghla trong SGK
Khdi da dien (H) dugc ggi Id khdi da dien ldi ne'u mdt dogn thdng ndi hai diem bdt ki thudc (H) deu ndm trgn trong (H).
H4. Hay ndu mgt sd vf du vd khdi da dien ldi.
26
»Thuc bien Al trong 5 phiit.
Hoat dgng cua GV
Cdu hoi I
Hay neu vf du vd khdi da dien ldi trong thuc te.
Cdu hoi 2
Hay neu vi du vd khdi da dien khdng ldi trong thuc te.
Cdu hoi 3
Neu su khac nhau giiia da dien ldi va da dien khdng ldi.
B
Hoat dgng cua HS
Ggi y trd ldi cdu hoi I
Hinh lap phuong (hop phan), hinh hop chii nhat...
Ggi y trd ldi cdu hoi 2
HS tu neu vi du bang dung cu thuc te,...
Ggi y trd ldi cdu hoi 3
HS tu tra Idi.
HOATDQNG 2
H. KHOI DA DifiN D£ U
• GV sit dung hinh 1.19 va neu cau hdi:
H5. Hinh lap phuong cd tfnh chat chung gi ve cac mat?
H6. Tii dien ddu cd tinh chat chung gi vd cac mat?
27
GV neu dinh nghia :
Khdi da dien diu Id khdi da dien ldi cd tinh chdt sau:
a) Mdi mat cua nd Id mot da gidc diu p cgnh.
b) Mdi dinh cua nd Id dinh chung cua diing q mat.
Khd'i da dien deu nhu vdy ngUdi ta ggi Id khd'i da dien diu logi {p, qj. H7. Mdi mat ciia khdi da dien ddu la nhiing da giac ddu bang nhau. Diing hay sai? H8. Cd ngii giac ddu khdng?
• GV neu dinh II:
Chi cd ndm logi da dien deu (3, 3), (4, 3), (3, 4), {5, 3} vd {3, 5). H8. Hay ve khdi da dien ddu {4, 3} va {3, 4}.
• GV gidi thieu mdt sd hinh anh vd da giac ddu ciia Le-d -na Do Vin -ci
a) b)
Kiioi da dien 12 mdt
28
: ^ ^
a) b)
Khd'i da dien deu 20 mat
• Thuc hien ^ 2 trong 5 phiit.
Hay cho HS tu ve bat dien ddu.
Hoat dgng cua HS
Hoat dgng cua GV
Ggi y trd ldi cdu hoi I
Cdu hoi 1
Hay de'm cac dinh cua bat dien
Gdm 6 dinh
ddu.
29
Cdu hoi 2
Hay dem cac canh ciia bat dien ddu.
• GV cho HS didn vao bang tdm tat sau:
Ggi y trd ldi cdu hoi 2 12 canh.
Loai {3,3} {4,3} {3,4} {5,3} {3,5}
Ten goi So dinh So canh So mat
• Thuc hien vi du 1 trong 15'
cau a. Su dung hinh 1.22 a trong SGK.
Hoat dgng cua GV
Cdu hoi I
Hay ve hinh va dat ten cho cac dinh cua bat dien.
Cdu hdi 2
Ke ten cac mat cua bat dien.
Thuc hien ^ 3 trong 5 phiit
30
Hoat dgng cua HS
Ggi y trd ldi cdu hoi I HS tu ve hinh va dat ten.
Ggi y trd ldi cdu hoi 2 HS tu liet ke toan bg
Hoat dgng ciia GV
Cdu hoi I
Hay chi ra mdt sd mat ciia bat dien.
Cdu hoi 2
Chiing minh cac mat ciia bat dien la cac tam giac ddu
cau b. Sii dung hinh 1.22 b trong SGK. Hoat dgng cua GV
Cdu hoi I
Hay ve hinh va dat ten cho cac dinh ciia bat dien.
Cdu hoi 2
Ke ten cac mat ciia bat dien.
Thuc hien ^ 4 trong 5 phiit.
Hoat dgng cua HS
Ggi y trd ldi cdu hoi 1
HS tu chi ra.
Ggi y trd ldi cdu hoi 2
Tam giac NEJ ching ban ta thay day la tam giac ddu canh —
Hoat dgng cua HS
Gen y trd ldi cdu hoi 1
HS tu ve hinh va dat ten.
Ggi y trd ldi cdu hoi 2
HS tu liet ke toan bd
31
A'
Hoat dgng ciia GV
Cdu hoi I
Hay chi ra mgt sd mat ciia bat dien.
Cdu hoi 2
Chiing minh cac mat ciia bat dien la cac tam giac ddu.
Hoat dgng ciia HS
Ggi y trd ldi cdu hoi I
HS tu chi ra.
Ggi y trd ldi cdu hoi 2
Tam giac NEJ chang ban ta thay day la tam giac ddu canh —
HOATDQNG 3
TdM TflT Bfll HPC
1. Khdi da dien (H) dugc ggi la khdi da dien ldi ndu mdt doan thang ndi hai diem bat ki thudc (H) ddu nam trgn trong (H).
2. Khdi da dien ddu la khdi da dien Idi cd tfnh chat sau:
a) Mdi mat cua nd la mdt da giac ddu p canh.
b) Mdi dinh cua nd la dinh chung ciia diing q mat.
Khdi da dien ddu nhu vay ngudi ta ggi la khdi da didn ddu loai (p, q}. 32
3. Chi cd nam loai da dien ddu {3,3}, {4,3}, {3,4}, {5,3} va {3,5}. HOAT DONG 4
MQT SO CflU HOI TRflC NGHIEM
Cdu I. Hay didn diing, sai vao cac d trdng sau day:
Cho hinh tur dien :
(a) Hinh tii dien cd 4 dinh
(b) Hinh tii dien cd 4 mat
(c) Hinh tii dien cd 4 canh
(d) Cac mat la nhiing tam giac
Trd ldi.
n D D
a D
b D
c S
d D
Cdu 2 Hay didn diing, sai vao cac d trdng sau day:
33
Cho hinh ve
(a) Cd mdt hinh bat dien cua hinh tren
(b) Hinh bat dien cd mdt mat la hinh vudng (c) Hinh bat dien cd tat ca cac mat la cac tam giac (d) Hinh bat dien dd cd the la hinh bat dien ldi Trd ldi.
D D D D
a D
b S
c
D
d D
Chgn cdu trd ldi ddng trong cdc bdi tap sau: .Cdu 3 Cho hinh ve:
34
--r C
(a) Hinh da cho la mdt khdi da dien ldi
(b) Hinh tren khdng the la khdi da dien Idi.
(c) Cac mat cua khdi da dien tren la nhiing tam giac
(d) Ca ba cau trdn deu sai.
Trd ldi (a).
Cdu 4. Cho hinh hop chii nhat ABCDA'B'CD'
D'
(a) Cac mat ciia hinh hop la hinh vudng.
(b) Cac mat ciia hinh hop la hinh tam giac.
(c) Cac mat ciia hinh hop la hinh chii nhat.
(d) Cac mat cua hinh hop la hinh thoi.
Trd ldi (c).
Cdu 5 Cho hinh chop ddu ABCD. Gdc ADB bang
D
(a) 60°; (b) 120°;
(c) 90"; (d) 150°
Trd ldi (a).
Cdu 6. Cho tii dien deu ABCD. Tdng ba gdc d dinh A la (a) 90° (b)180°
(c) 45° (d) 30°
Trdldi (b).
Cdu 7. Cho mdt bat dien ddu. Mdi gdc tai mdt dinh cua mdt mat la (a) 90° (b) 60°
(c) 45° (d) 30°
Trd ldi (b).
HOAT DONG 6
mtftiQ DflN GIfll Bfll TAP SflCH GIflO KHOfl Bai 1. Day la bai tap thuc hanh. GV yeu cau HS ga'p giay va thuc hien.
36
/
/ ' ^
/ B
/
A
D
b)
c)
GV dat cac cau hdi sau :
Hoat ddng cua GV
Cdu hoi 1
0 hinh thii nhat sau khi cat va gap
ta dugc hinh gi?
Cdu hoi 2
0 hinh thii hai sau khi cat va ga'p
ta dugc hinh gi?
Cdu hoi 3
6 hinh thii ba sau khi cat va ga'p
ta dugc hinh gi?
Bai 2. Sit dung vf du 1.
37
Hoat dgng cua HS
Ggi y trd ldi cdu hoi I Hinh tii dien deu, hinh a)
Ggi y trd ldi cdu hoi 2 Hinh lap phuong, hinh b).
Ggi y trd ldi cdu hoi 3 Hinh bat dien ddu, hinh c).
Hoat dgng cua GV
Cdu hoi I
Ggi canh ciia hinh lap phuong la a. IMi dien tich toan i^hin cua hinh (H). Cdu hdi 2
Hay tinh canh cua hinh bat dien.
Cdu hdi 3
Tinh dien tfch toan phan ciia hlnh (H').
Cdu hdi 4
Tfnh ti sd dien tfch toan phan cua hinh(H)va (H').
Bai 3. Sii dung tinh chat cua tii dien ddu. 38
Hoat ddng ciia HS
Ggi y trd ldi cdu hoi 1
S = 6al
Ggi y trd ldi cdu hoi 2
aV2
Canh cua hinh bat dien la 2
Ggi y trd ldi cdu hoi 3
S'= a^Vs.
Ggi y trd ldi cdu hoi 4
^ = 2V3
S'
Hoat ddng cua GV
Cdu hdi I
Ggi canh ciia hinh tii dien ddu la
a. Tfnh canh ciia hinh MNEF
Cdu hoi 2
Chiing minh • MNEF la hinh tir
dien ddu.
Bai 4. Sit dung tinh chat cua bat dien ddu.
39
Hoat dgng cua HS
Ggi y trd ldi cdu hdi I
NM = -3
Ggi y trd ldi cdu hoi 2
Chiing minh cac canh bang nhau.
Cau a)
Hoat dgng cua GV
Cdu hoi 1
Chiing minh B, C, D, E thudc mat phing trung true cua AF.
Cdu hdi 2
Hay chifng minh EC, BD va AF ddng quy.
Cdu hdi 3
Chung minh cau a).
caub)
Hoat dgng cua GV
Cdu hdi I
Chiing minh ABFD la hinh vudng.
Cdu hdi 2
Chiing minh cau b).
40
Hoat ddng ciia HS
Ggi y trd ldi cdu hdi 1
HS tu chiing minh.
Ggi y trd ldi cdu hoi 2
Ta tha'y BODE la hinh thoi nen BD va CE cat nhau tai trung diem I ciia mdi dudng.
ABFD ciing la hinh thoi nen AF va BD ciing cit nhau tai trung diem I.
Ggi y trd ldi cdu hdi 2
HS tur chiing minh.
Hoat ddng cua HS
Ggi y trd ldi cdu hoi I
HS tu chiing minh AF = BD Tuf dd ta cd ABFD la hinh thoi cd hai dudng cheo bang nhau.
Ggi y trd ldi cdu hdi 2
HS tu chiing minh.
§3. Khai niem the tich cua khoi da dien (tiet 6, 7, 8)
1. MUC Tl£u
I. Kien thufc
HS nam dugc:
1. Khai niem the tfch cua khdi da dien.
2. Cac cdng thiic tinh the tfch ciia mdt sd khdi da dien cu the.
3. Tinh chat va the tfch ciia khdi lang tru, khdi chdp.
2. KI nang
• Tfnh dugc the tfch hinh lang tru, hinh chdp.
• Tfnh dugc ti sd the tfch cac khdi da dien dugc tach ra tix mdt khdi da dien. 3. Thai do
• Lien he dugc vdi nhidu va'n dd cd trong thuc te vd khdi da dien. • Cd nhidu sang tao trong hinh hgc.
• Hiing thii trong hgc tap, tfch cue phat huy tfnh ddc lap trong hgc tap.
n. CHUAN BI CUA GV VA m
1. Chuan bi cua GV:
• Hinh ve 1.256 den 1.28 trong SGK.
• Thudc ke, phah mau,...
• Chu^ bi san mdt vai hinh anh thuc te vd khdi da didn.
2. Chuan bj cua HS
Dgc bai trudc d nha, dn tap lai mgt sd tfnh chat ciia khdi lang tru, khdi chdp. 41
in. PHAN PHOI THCbl LUONG
Bai nay chia thanh 3 tiet:
Tie't 1 : Tii dau de'n bet phan I.
Tiet 2 : Phin II.
Tie't 3 : Phan III
IV. TIEN TPINH DAY HOC
n. t)RT vnN f>€
Cau hdi 1.
Neu cdng thiic tfnh the tich mdt sd hinh ma em da hgc
Cau hdi 2.
Thd tfch hinh lap phucmg canh bang a la bao nhieu ?
Cau hoi 3.
Hai hinh lap phuong bang nhau thi the tfch bang nhau. Diing hay sai? Cau hdi 4.
Em cd nhan xet nhiing hinh nhu the nao thi cd thd tfch.
0. sni M6 I
HOATDQNGl
I. KHAI NifiM Nt THfi TICH KHOI DA DifeN
• GV dat ra mdt sd tinh hudng:
HI. Hinh lap phuong cd canh bing 1 thi the tfch la bao nhieu? H2. Hai khdi da dien bing nhau lieu thd tfch cd bing nhau khdng? H3. Neu khdi da dien dugc phan chia thanh hai khdi da dien thi quan he the tfch giiia chiing nhu the nao ?
42
GV dua ra ba md hinh the hien cho ba y tren bing hinh anh sau:
----^ z:===-
1 J- - -
__.-—^
a)
y^\""-
1 , -
,5,-5.'^'*''~'
r2)
Sd duang V,^^^ ndi tren dugc ggi Id the tich ciia khd'i da dien (H). The tich khdi lap phuang cd cgnh la 1 ggi la khdi lap phuang dan vi.
43
• GV neu vf du, phan tfch cac hinh d hinh 1.25 va ndu cac cau hdi: H4. Khdi da dien nao la khdi lap phuong don vi?
H5. Lieu mgi khdi da dien cd the tfnh the tfch qua khdi lap phuong don vi dugc hay khdng?
• Thuc hien ^ 1 trong 3 phiit.
(Ho)
Hoat dgng cua GV
Cdu hoi 1
Trong hinh (H,) cd bao nhieu hinh lap phuong ?
Cdu hdi 2
Trong hinh (Hi) cd bao nhieu hinh (Ho).
Cdu hdi 3
Tfnh V(j^^) theo V^^^)
GV ndu ke't luan :
(H,)
Hoat dgng ciia HS
Ggi y trd ldi cdu hdi I 5 hinh lap phuong.
Ggi y trd ldi cdu hoi 2 Cd 5 hinh (H^).
Ggi y trd ldi cdu hdi 2 >,)=5>. )
Ggi (H,) Id khd'i hop chii nhdt kich thdc a = 5,b = l,c = l. Thuc hien A 2 trong 3 phiit.
^ / / / /
/
/ / / / /
/
/ / / / /
/
/ / / / /
(H,) (Ha)
44
Hoat ddng cua GV
Cdu hdi I
Trong hinh (H2) cd bao nhieu hinh (H,) ?
Cdu hdi 2
Trong hinh (H2) cd bao nhieu hinh (Ho).
Cdu hdi 3
Tinh V(jj^) theo V(H^).
• GV neu ke't luan :
Hoat ddng ciia HS
Ggi y trd ldi cdu hoi I 4 hinh lap phuong.
Ggi y trd ldi cdu hdi 2 Cd 20 hinh (Ho).
Ggi y trd ldi cdu hdi 2 > . ) =" • >, )
Ggi (H2) Id khdi hop chii nhdt kich thdc a = 5,b = 4,c = 1. • Thuc hien ^ 3 trong 3 phiit.
X / y / / / / / / /
/^ / / / / / y / / / / / / /
/
/
v
/ / / /
/
/ / / / / /
/
/
/
/
/
V
/
(Hj)
(H)
Hoat dgng cua GV
Cdu hdi 1
Trong hinh (H) cd bao nhieu hinh (H^)?
Cdu hdi 2
Trong hinh (H) cd bao nhieu hinh (Ho)?
Cdu hdi 3
Tinh V(H) theo V(H^).
Hoat dgng cua HS
Ggi y trd ldi cdu hdi I
4 hinh (Hj).
Ggi y trd ldi cdu hdi 2
Cd 60 hinh (Ho).
Ggi y trd ldi cdu hdi 2
V(H)-3.V(H^)
45
• GV neu ke't luan :
Ggi (H) la khdi hop chu nhdt kich thudc a = 5,b = 4,c = 3. • GV ke't luan :
V(H)= a.b.c
• GV neu dinh If:
The tich ciia khdi hop chit nhdt bdng tich cua ba kich thudc. • Mdt so cau hdi ciing cd :
H6. Hinh hop cd kfch thudc 1, 2, 3 cd the tfch la 6.
(a) Dung (b) Sai.
H7. Hinh hop cd kfch thudc 2, 3, 4 cd the tfch la 24. (a) Diing (b) Sai.
H8. Hinh hop cd kfch thudc 4, 2, 3 cd the tfch la 24. (a) Diing (b) Sai.
H9. Hinh hop cd kfch thudc 5, 2, 3 cd the tfch la 30. (a) Diing (b) Sai.
HIO. Hinh hop cd kfch thudc - , 2, 3 cd thd tfch la 3.
(a) Diing (b) Sai.
3 Hll. Hinh hop cd kfch thudc 1,2, — cd the tfch la 3. (a) Diing (b) Sai.
HI2. Hinh hdp cd kfch thudc 1, - . 3 cd thd tfch la 1. 3
(a) Dung (b) Sai.
46
HOATDQNG 2
H. THE TICH KHOI LANG TRU
H12. Hinh hop chii nhat cd phai la hinh lang tru khdng?
H13. Hay tfnh dien tfch day S cua hinh (H).
H14. Hay tfnh chidu cao h ciia hinh (H).
HI5. Hay tfnh Sh.
Hld.^So sanh thd tfch ciia (H) va S.h.
• GV neu van dd : Ngoai nhung hinh dac biet nhu hinh hop chii nhat, mgi hinh lang tni cd the tich nhu vay.
• GV neu dinh II:
The tich khdi ldng tru cd dien tich ddy B vd chieu cao h IdV = B.h. • Mdt sd cau hdi ciing cd
H17. Hinh lang tru cd dien tfch day la 8 chidu cao 7 cd thd tfch la 56. (a) Diing (b) Sai.
H18. Hinh lang tru cd dien tfch day la — chidu cao 8 cd the tfch la 4. (a) Diing (b) Sai.
H19. Hinh lang tru cd dien tich day la 8 chidu cao — cd the tfch la 4.
(a) Diing (b) Sai.
3 H20. Hinh lang tru cd dien tfch day la 8 chieu cao — cd the tfch la 12. (a) Dung (b) Sai.
47
HOATD(DNG3
III. THE TICH HINH CHOP
• GV neu dinh 11:
The tich khdi chdp cd dien tich ddy Id B, chieu cao h la
V = -B.h.
3
• Thuc hien ^ 3 trong 3 phiit.
Hoat dgng cua GV
Cdu hdi 1
Tfnh dien tfch day ciia Kim tu thap.
Cdu hdi 2
Tfnh the tfch khdi chdp Kim tu thap.
Hoat ddng cua HS
Ggi y trd ldi cdu hdi I
B = 230.230= 113400 m'
Ggi y trd ldi cdu hdi 2
V= -.113400. 147 401200m' 3
• Thuc hien vf du trong 5'. Sit dung hinh 1.28 trong SGK. cau a.
Hoat ddng cua GV
Cdu hdi I
Hay tinh the tfch khdi chdp :
C. A'B'C theo V.
Cdu hdi 2
Hay tinh the tfch khdi chdp :
C. A'B'BA theo V
Cdu hdi 3
So sanh the tfch ciia hai khdi C.ABFE va C.A'B'FE.
48
Hoat ddng ciia HS
Ggi y trd ldi cdu hdi I
\c. A'B'C ) ~ T ^
Ggi y trd ldi cdu hdi 2
1 2 V/ x = V--V - — V ^(C. A'B'BA ) ^ 3 3
Ggi y trd ldi cdu hdi 3
Thd tfch hai khdi nay bing nhau..
Cdu hdi 4
Hay tfnh the tfch khdi chdp : C. ABFE theo V.
caub.
Hoat ddng cua GV
Cdu hdi 1
Hay tfnh the tfch ciia (H)
Cdu hdi 2
Hay tfnh thd tfch khdi chdp : C. C'E'F' theo V.
Cdu hdi 3
Tfnh ti sd hai the tich da cho.
Ggi y trd ldi cdu hoi 4
X(CABFE) ""3 ^
Hoat ddng cua HS
Ggi y trd ldi cdu hdi I
V(„, = v-iv = fv
Ggi y trd ldi cdu hdi 2
4
^(C.CE'F) "^ ^-^(CCA'B') "^ T ^ Ggi y trd ldi cdu hdi 3
V, 1
V2 2
HOATDQNG 4
TbM TflT Bfll HQC
1. a) Ndu (H) la khdi lap phucmg cd canh la 1 thi V/^jx = 1.
b) Nd'u (H) = (H) thi V(H) = V(H,)
c) Nd'u (H) dugc phan chia thanh hai khdi da dien (H,) va (Hj) thi V(H)-V(H,)+V(H^)
Sd ducmg V^H) "oi ^r^" ^^bc ggi la thd tfch cua khdi da didn (H). Thd tich khdi lap phucmg cd canh la 1 ggi la khdi lap phuong don vi.
49
2. Thd tfch ciia khdi hdp chii nhat bing tfch ciia ba kfch thudc. 3. Thd tfch khdi lang tru cd didn tfch day B va chieu cao h la V = B.h. 4. The tfch khdi chdp cd didn tfch day la B, chidu cao h la
V=-B.h.
3
HOAT DONG 3
MQT SO CflU H6 | TRflC NGHIEM
Hay dien dung (D), sai (S) vao cac khang dinh sau :
Cdu 1. Cho hinh ve ciia mdt hinh bat dien ddu cd the tfch la V A
(a) V,
V
D
'(A.BCDE) ~ 2
(b) V,
_ v_
D
"(F.BCDE) ~ 2
V
(C) ^(A.BCE)=' ^
V
(d) V(A.ciD)=y 50
D
D
^
Trd ldi.
a D
b D
c
D
d D
Cdu 2 Cho hinh ve cua mdt hinh bat dien ddu cd the tich la V
^^) Y(A.BCDE) ~ ^(F.BCDE)
(b) ^(A.CDE) "= '^(A.BCE)
^^' ^(A.CDE) ~ ^(F.BCE)
(") ^(F.CDE) ~ ^(A.BCE)
Trd ldi.
D D D D
a D
b D
c
D
d D
Cdu 3 . Cho hinh ve la hinh chdp tii giac ddu cd thd tich la V
51
(a) ^(S ABC) "^(S.DBC)
(b) V(s DOA) = '^(S.BOC) (C) %AOC) = VDB )
(d) '^(S.CDO) " '^(S.BCO) Trd /oi
Q D
D n
a
D
b
D
c
D
d
D
Chgn cdu trd ldi ddng trong cdc cdu sau: Cdu 4. Cho hinh lang tru cd thd tfch la V
Hinh sau cd thd tfch khdng phai la —
(a) A'. ABC
(c) B. A'B'C
Trdldi (d).
52
(b) C. ABC (d) A'. BCCB'.
Cdu 5 . Cho hinh lang tru c6 th^ tfch la V.
2V
PTuih sau c6 thd tfch Ik
(a) A'. ABC
(c) B. A'B'C
Trd ldi. (d).
Cdu 6 . Cho hinh vg :
Hinh trdn c6 thd tfch Ik
(b) C. ABC (d) A'. BCCB'.
(a) abc
(c) —abc 2
Trd ldi. (d).
(b)bca
(d) -abc
3
53
Cdu 7 Cho hinh ve vdi E, F la trung didm ciia cae canh SB va SC. s
Khdi S.AEF cd the tich la
(a) abc
(c) — abc Trd ldi. (b).
(b) — bca 24
(d) —abc 12
Cdu 8. Cho hinh ve vdi E, F la trung diem cua cac canh SB va SC. s
Khdi AEFCB cd the tich la
(a) abc
(c) — abc 8
Trd ldi (c). 54
(b) — bca 12
(d) —abc 12
Cdu 9. Cho hinh chdp S.ABCD nhu hinh ve. Day ABCD la hinh vudn^^, c^nh a s
Canh SA bing :
(a) a; (b) 2a;
(c) aV2 ; (d) a^B
Trd ldi. (d).
Cdu 10. Cho hinh chdp S.ABCD nhu hinh ve. Day ABCD la hinh vudng canh a. s
Thd tfch khdi chdp la
(a)a^ (b)ia^
(c) i^V2 (d) a'S
Trd ldi. (d).
55
Cdu 11 . Cho hinh chdp S.ABCD, day ABCD la hinh vudng canh a (hinh ve) S
The tfch hinh chdp S.BCD la
(a)a^ (c)
(b)ia^
6
'VI (d) 'V^ 6 ' 6
Trd ldi. (d).
Cdu 12. Cho hinh hdp canh la 1, 2, 3 nhu hinh ve. B; c
A'
Thd tfch khdi chdp D.AA'B' la
(a)0
(c)2
Trd ldi. (b). 56
(b)l (d)3.
Cdu 13 Cho hinh hdp canh la 1, 2, 3 nhu hinh ve. B' C
The tfch khdi hop chit nhat la
(a) 3 (b) 4
(c) 5 (d) 6. Trdldi (d).
Cdu 14. Cho hinh hdp canh la 1, 2, 3 nhu hinh ve.
B" C
A'. ^^^^ ^^ ^^^ 1 \ ^^^^
7\'3 \ ' ^< v ^ ' l \ •• / 1 ^ ^ >
/ 1 ^ v ^ ^ I 1 .>5--^-'2 . ! y B x \
D'
- ^
ti sd thd tfch ciia khdi chdp D.AA'B' va phin cdn lai la
(b)
1
<
(c) 1
Trd ldi. (b).
57
y.
HOATDCDNG 3
naOFNG DflN GIfll Bfll T6P SflCH GIflO KHOfl
Bai 1. Sii dung true tie'p cdng thiic tfnh the tfch khdi chdp. s
Gia sii ta cd tti dien ddu S.ABC canh a.
Hoat ddng cua GV
Cdu hdi 1
Hay tfnh canh AI.
Cdu hdi 2
Hay tfnh dien tich day.
Cdu hdi 3
Tfnh dudng cao SH.
Cdu hdi 4
Tfnh thd tfch hinh chdp. 58
Hoat ddng cua HS
Ggi y trd ldi cdu hdi I
2
Ggi y trd ldi cdu hdi 2
4
Ggi y trd ldi cdu hdi 3 f—
SH = VSA2 AH2="^ V 3
Ggi y trd ldi cdu hdi 4 a3V2
12
Bai 2. Su dung true tie'p cdng thiic tinh thd tfch khdi chdp. A
Gia sit ta cd bat dien ddu canh a nhu hinh ve.
Hoat ddng cua GV
Cdu hdi I
Chia bat dien ddu thanh hai khdi chdp tii giac ddu canh a. Chiing minh the tfch hai khdi chdp bing nhau.
Cdu hdi 2
Hay tfnh dien tich day.
Cdu hdi 3
Tfnh dudng cao AI.
Cdu hdi 4
Tfnh thd tfch hinh chdp.
Hoat ddng cua HS
Ggi y trd ldi cdu hdi I
HS tu chiing minh..
Ggi y trd ldi cdu hdi 2
S=a 2
Ggi y trd ldi cdu hdi 3
aV2 Al = ^ ^
2
Ggi y trd ldi cdu hdi 4
a^V2 V= Tuf dd suy ra thd tfch khdi 6
bat dien ddu.
59
Bai 3. Sit dung true tie'p cdng thiic tfnh thd tfch khdi chdp va thd tfch hinh hgp. B' C
Gia sit ta cd hinh ve.
Hoat ddng ciia GV
Cdu hdi I
Chiing minh cac thd tfch eac tii didn : AA'B'D' CC'B'D' D'ADC, B'ABC bing nhau.
Cdu hdi 2
Gia sit thd tfch hinh hop la V thi the tfch mdi hinh tren la bao nhieu?
Cdu hdi 3
Thd tfch hinh chdp ACB'D' la bao nhieu?
Cdu hdi 4
Tfnh tl sd hai thd tfch
60
Hoat ddng ciia HS
Ggi y trd lai cdu hdi I HS tu chiing minh.
Goi y trd ldi cdu hdi 2 iv
6
Ggi y trd ldi cdu hoi 3
1 V
V -v. 3 = — 3
Ggi y trd ldi cdu hdi 4 Ti sd 3.
Bai 4. Hudng ddn. Sit dung true tidp cdng thiic tfnh thd tfch hinh chdp A
Gia s\l ta cd hinh ve.
Hoat ddng ciia GV
Cdu hdi I
Chiingminh^^SB'C=SB'.SC' ^ASBC SB.SC
Cdu hdi 2
Chiing minh — =
h SA
Cdu hdi 3
Chiing minh bai toan trdn.
Hoat ddng cua HS
Ggi y trd ldi cdu hdi I
HS tu chiing minh bing each ve them dudng cao ciia mdi tam giac tii C va C
Ggi y trd ldi cdu hdi 2
HS tu chiing minh.
Ggi y trd ldi cdu hdi 3
HS tu chiing minh.
Bai 5. Hudng ddn. Six diing true tidp cdng thiic tfnh thd tfch hinh chdp D
Gia sii ta cd hinh ve.
61
Hoat ddng cua GV
Cdu hdi I
Chirng minh CE 1 mp(ABD).
Cdu hdi 2
DA
Cdu hdi 3
T'v, DF Tmh DB
Cdu hdi 4
rr- u. ' - u -.u^'.' u VEFC ) Tinh tl so hai the tich ^(DBAC)
Cdu hdi 5
Tinh thd tfch tii dien CDEF.
Hoat ddng cua HS
Ggi y trd ldi cdu hdi I
^ , JBAIAC ^^ , _ Ta CO -^ => BA -L CE [BA 1 DC
Lai cd CE ± AD nen AD l mp(DAB). Ggi y trd ldi cdu hdi 2
CD^
DE DA _ a^ _ 1
DA DA 2a^ 2
Ggi y trd ldi cdu hdi 3
DF CD^ a^ 1
DB DB^ 3a2 3
Ggi y trd ldi cdu hdi 4
'^(DEFC) DF.DE.DC _ 1
V(DBAC) DB.DA.DC 4
Ggi y trd ldi cdu hdi 5
1 1 3
VEF)=4^^^ ^
B^i 6. Hudng ddn. Six dung true tie'p cdng thiic tfnh thd tfch hinh chdp
Gii sft ta cd hkih ve.
62
Hoat ddng cua GV
Cdu hdi I
Chiing minh thd tfch hai khdi chdp DABC va DCBE bing nhau.
Cdu hdi 2
Chiing minh thd tfch khdi chdp DCBE khdng ddi.
Hoat ddng cua HS
Ggi y trd ldi cdu hdi I
HS tu chiing minh.
Ggi y trd ldi cdu hdi 2
Tam giac ECD cd EC = a, CD = b. ECD = (d,d') khdng ddi do dd dien tfch tam giac ECD khdng ddi. Dudng cao ha tit B de'n day (ECD) la khoang each giiia d va mp(ECD) khdng ddi.
Tii dd ta dugc dpcm.
63
On tap chrfcrng I
(tiet 9,10)
I. MUG Tl£u
1. Kien thurc
HS nam dugc:
Khai niem :
+. Hinh da dien va khdi da dien trong khdng gian.
+ Hai khdi da didn bing nhau.
+ Phan chia mdt khdi da dien thanh nhidu khdi da didn khac nhau. + Khdi da dien Idi
+ Khdi da dien ddu.
+ Thd tfch cac khdi da didn : Thd tfch hinh hdp, hinh chdp va hinh lang tni. Mdt sd dinh If va mdnh dd quan trgng:
+ Qua phep ddi hinh thi ta dugc hai khdi da didn bing nhau.
+ Hai khdi da didn bing nhau thi cd thd tfch bing nhau.
+ Chi cd 5 loai khdi da didn ddu.
+ Thd tfch hinh hop, hinh chdp va hinh lang tru.
2. KT nang
• Tfnh thanh thao the tfch mdt sd khdi da didn : Hinh hdp chii nhat, khdi chdp va khdi lang tru.
• Mdl quan he giiia the tfch cua cac khdi dd.
• Mdl quan hd gifla the tfch va didn tfch.
• Mdi quan hd giua thd tfch va khoang each.
64
3. Thai do
• Lidn he dugc vdi nhidu vah dd cd trong thuc te vdi mdn hgc hinh hgc khdng gian. • Cd nhidu sang tao trong hinh hgc.
• Hiing thii trong hgc tap, tfch cue phat huy tfnh dgc lap trong hgc tap.
n. CHUXN BI CUA GV VA n&
1. Chuan bi ciia GV:
• Chuin bi dn tap toan bd kien thiic trong chucmg.
• Chudn bi mdt den hai bai kidm tra.
• Cho hgc sinh kiem tra va chain, tra bai.
2. Chuan bi ciia HS :
On tap lai toan bd kie'n thiic trong chuong, giai va tra ldi cac cau hdi bai tap trong chuang.
in. PHAN PHOI TH6I LUONG
Bai nay chia thanh 2 tie't:
Tiet 1 : On tap.
Tiet 2 : Kidm tra 1 tiet.
IV. TifN TDlNH DAY HOG
n. DMT VPTN D €
cau hdi 1.
Em hay nhic lai: Cac khai nidm khdi da dien, khdi chdp, khdi lang tru va khdi hop chii nhat.
cau hoi 2.
Ndu mdl quan he giita thd tfch khdi lang tru va khdi chdp cd cung day. cau hdi 3.
Hay nhic lai cac khai- nidm khoang each. Tit dd em cd them phucmg phap nao tfnh khoang each dua vao thd tfch.
65
HOAT CHDNG 1
1. On tap kien thiirc ccJ ban trong chi/dng
a) Tdm tat li thuye't co ban.
1. a) Hai da giac phan biet chi cd the : Hoac khdng cd didm chung hoac cd mdt canh chung.
b) Mdi canh ciia da giac nao cung la canh chung cua diing hai da giac. 2. ITinh da dien la hinh dugc tao bdi cac da giac thda man 2 tfnh chit tren.
Khdi da dien la phan khdng gian dugc gidi ban bdi hinh da dien, kd ca hinh da dien do.
3. Trong khdng gian, quy tic dat tuong ung mdi didm M vdi duy nhat mdt didm M' dugc ggi la phep bien hinh trong khdng gian.
Phep bien hinh trong khdng gian la phep ddi hinh ne'u nd bao toan khoang each.
4. Phep tinh tien theo vecto v la phep bien hinh bie'n M thanh M' ma MM' = v
5. Phep ddi xiing tam O la phep bien hinh bien O thanh chfnh nd. Bie'n mdi didm M khac O thanh M' ma O la trung diem ciia MM'
6. Phep ddi xiing qua dudng thing A la phep bie'n hinh bie'n mdi didm thudc A thanh chinh nd. Bien mdi didm M khdng thudc A thanh didm M' ma A la dudng trung tryc cda MM'
7. Thuc hien lien tiep cac phep ddi hinh ta dugc phep ddi hinh.
Phep ddi hinh bien da dien (H) thanh da dien (H') va dinh, canh, mat ciia (H) thanh dinh, canh, mat ciia (H').
8. Hai hinh dugc ggi la bing nhau neu nd cd mdt phep ddi hinh bie'n hinh nay thanh hinh kia.
66
9. Khdi da didn (H) dugc ggi la khdi da dien ldi ne'u mdt doan thing ndi hai didm ba't ki thudc (H) ddu nim trgn trong (H).
10. Khdi da didn ddu la khdi da didn ldi cd tfnh chat sau:
a) Mdi mat ciia nd la mdt da giac ddu p canh.
b) Mdi dinh ciia nd la dinh chung cua diing q mat.
Khdi da didn ddu nhu vay ngudi ta ggi la khdi da dien ddu loai {p, q}. 11. Chi cd nam loai da didn ddu {3,3}, {4,3}, {3,4}, {5,3} va {3,5}.
12. a) Nd'u (H) la khdi lap phuong cd canh la 1 thi Ny^^ = 1.
b)Nd'u(H) = (H') thi V(H) = V(H,)
c) Neu (H) dugc phan chia thanh hai khdi da dien (H,) va (H2) thi V(H)=V(H,)+V(H^)
Sd duong V/^\ ndi trdn dugc ggi la thd tfch cua khdi da dien (H).
Thd tfch khdi lap phuong cd canh la 1 ggi la khdi lap phuong don vi. 13. Thd tfch cua khdi hdp chii nhat bing tfch cua ba kfch thudc. 14. Thd tfch khdi lang tru cd didn tfch day B va chidu cao h la V = B.h. 15. Thd tfch khdi chdp cd didn tfch day la B, chidu cao h la
V--B.h .
3
b) cau hdi tr^c nghiem nh^m dn tap kie'n thurc:
GV ndn dua ra mdt he thdng cau hdi trie nghiem nhim dn tap toan bd kie'n thiic trong chuong.
Sau day xin gidi thidu mgt sd cau hdi:
67
L HAY KHOANH TRON CAU DUNG, SAI TRONG CAC CAU SAU MA EM CHO LA HOP LL
Cdu 1. Mgi phep bien hinh deu dugc hai khdi da dien bang nhau. (a) Diing (b) Sai.
Cdu 2. Phep tinh tien theo vecto v ddu dugc hai khdi da dien bing nhau. (a) Diing (b) Sai.
Cdu 3. Phep ddi xiing tam O dugc hai khdi da dien bing nhau. (a) Diing (b) Sai.
Cdu 4. Phep ddi xiing qua dudng thing dugc hai khdi da dien bing nhau. (a) Diing (b) Sai.
Cdu 5. Phep ddi xiing qua mat phang dugc hai khdi da dien bing nhau. (a) Diing (b) Sai.
Cdu 6. Qua hai phep bien hinh : Phep tinh tie'n theo vecto v va phep ddi xiing tam O dugc hai khdi da dien bing nhau.
(a) Diing (b) Sai.
Cdu 7. Qua hai phep bien hinh : Phep tinh tie'n theo vecto v va phep ddi xung qua dudng thing dugc hai khdi da dien bing nhau.
(a) Diing (b) Sai.
Cdu 8. Qua hai phep bie'n hinh : Phep ddi xiing tam O va phep ddi xiing qua dudng thing dugc hai khdi da dien bing nhau.
(a) Diing (b) Sai.
Cdu 9. Khdi da dien ludn chiia trgn mgi doan thing cd hai diu thudc khdi da dien la khdi da dien ldi.
(a) Diing (b) Sai.
Cdu 10. Khdi da dien ludn chiia trgn mgi dudng thing la khdi da dien Idi. (a) Diing (b) Sai.
Cdu 11. Khdi tii dien cd 4 mat la tam giac ddu la khdi da dien ddu (a) Dung (b) Sai.
Cdu 12. Co vd sd khdi da dien ddu
(a) Diing (b) Sai.
68
Cdu 13. Chi cd 5 khdi da dien ddu
(a) Dung (b) Sai.
Cdu 14. Khdi da dien ddu cd sd dinh va sd mat bing nhau
(a) Dung (b) Sai.
Cdu 15. Da dien cd cac mat la tam giac thi tdng sd cac mat phai la sd chan. (a) Dung (b) Sai.
Cdu 16. Da dien cd mdi dinh la dinh chung cua sd mat le thi tdng sd cac dinh phai la sd chan.
(a) Diing (b) Sai.
Cdu 77.'Trung didm cac canh ciia mdt tii dien ddu la dinh ciia mdt tii dien deu. (a) Diing (b) Sai.
Cdu 18. Hinh lap phuong la mdt da dien ddu.
(a) Diing (b) Sai.
Cdu 19. Hinh lap phuong la luc dien ddu.
(a) Dung (b) Sai.
Cdu 20. Hinh lap phuong la da dien ddu dang {12, 8}
(a) Diing (b) Sai.
Cdu 21. Hinh lap phuong la da didn ddu dang {4, 3}
(a) Dung (b) Sai.
Cdu 22. Hinh lap phuong la da dien ddu dang {3,4}
(a) Diing (b) Sai.
Cdu 23. Hinh bat dien ddu la da dien ddu dang {4,3}
( a) Diing (b) Sai.
Cdu 24. Hinh bat dien ddu la da dien ddu dang {4,3}
(a) Diing (b) Sai.
Cdu 25. Hinh 12 mat ddu la da dien ddu dang {5,3}
(a) Diing (b) Sai.
69
Cdu 26. Hinh 12 mat ddu la da dien ddu dang {3, 5} (a) Diing (b) Sai. Cdu 27. Hinh 20 mat ddu la da dien ddu dang {3,5} (a) Diing (b) Sai. Cdu 28. Hinh 20 mat ddu la da dien ddu dang {5,3} (a) Diing (b) Sai. Cdu 29. Hinh hop chu nhat kfch thudc 2, 3, 4 cd thd tfch la 24 (a) Dung (b) Sai. Cdu 30. Hinh hop chit nhat kfch thudc 2, 3, 4 cd thd tfch la 12 (a) Diing (b) Sai. Cdu 31. Hinh lang tru la hinh hop.
(a) Dung (b) Sai. Cdu 32. Hinh lap phuong la hinh lang tru
(a) Diing (b) Sai. Cdu 33. Trong hinh lang tru dimg, cac mat ben vudng gdc vdi day. (a) Diing (b) Sai. Cdu 34. Trong hinh lang tru diing, cac canh ben song song vdi nhau. (a) Diing (b) Sai. Cdu 35. Trong hinh lang tru diing, cac each ben vudng gdc vdi day. (a) Diing (b) Sai. Cdu 36. Hinh hop chii nhat cd cac mat ben la hinh chii nhat. (a) Dung (b) Sai. Cdu 37. Hinh lap phuong cd cac mat la hinh vudng.
(a) Diing (b) Sai. Cdu 38. Hinh chdp ddu cd cac mat ben la tam giac ddu. (a) Diing (b) Sai. Cdu 39. Hinh chdp ddu cd cac mat ben la tam giac can. (a) Dung (b) Sai.
70
Cdu 40. Hinh chdp tii giac ddu la hinh chdp ddu
(a) Dung (b) Sai.
Cdu 41. Hinh chdp tii giac ddu canh a cd thd tich la - a
(a) Diing (b) Sai.
Cdu 42. Mdt hinh chdp cd chung day vdi hinh lang tru. Dinh cua hinh chdp thugc day cdn lai cua hinh lang tru. The tfch khdi lang tru va khdi chdp bing nhau (a) Dung (b) Sai.
Cdu 43. Mdt hinh chdp cd chung day vdi hinh lang tru. Dinh cua hinh chdp thudc day cdn lai ciia hinh lang tru. Thd tich khdi lang tru gap 3 lan khdi chdp.
(a) Dung (b) Sai.
Cdu 44. Mdt hinh chdp cd chung day vdi hinh lang tru. Dinh ciia hinh chdp thugc day cdn lai ciia hinh lang tru. The tich khdi lang tru gap 6 lan khdi chdp.
(a) Diing (b) Sai.
Cdu 45. Hinh lang tru cd dien tich day la 6, the tich la 24. Khoang each tir mdt didm ciia day nay de'n day kia la 4
(a) Diing (b) Sai.
Cdu 46. Hinh lang tru cd dien tich day la 6, the tich la 24. Khoang each tir mdt didm cua day nay de'n day kia la 6
(a) Diing (b) Sai.
Cdu 47. Hinh lang tru cd dien tfch day la 6, the tfch la 24. Khoang each tir mgt didm cua day nay de'n day kia la 12
(a) Dung (b) Sai.
Cdu 48. Hinh chdp cd dien tfch day la 6, the tfch la 24. Khoang each tir dinh de'n day la 6
(a) Diing (b) Sai.
Cdu 49. Hinh chdp cd dien tfch day la 6, thd tfch la 24. Khoang each tir dinh den day la 12
(a) Dung (b) Sai.
71
Cdu 50. Hinh chdp cd dien tfch day la 6, thd tfch la 24. Khoang each tii dinh de'n day la 18
(a) Diing (b) Sai.
Cdu 51. Cho OA, OB va OC ddi mdt vudng gdc vdi nhau, H la true tam tam giac ABC. Khi dd HO 1 (ABC).
(a) Diing (b) Sai.
Cdu 52. Mdt tii dien ed ba canh ddi mdt vudng gdc vdi nhau ggi la tii didn vudng. Tii dien vudng la tii dien ddu.
(a) Dung (b) Sai.
Cdu 53. Tii dien vudng la hinh chdp ddu.
(a) Diing (b) Sai.
Cdu 54. Tix dien vudng cd ba mat la cac tam giac vudng.
(a) Diing (b) Sai.
Cdu 55. Tii dien ddu cd cac mat la eac tam giac ddu.
(a) Dung (b) Sai.
Cdu 56. Hinh chdp tam giac ddu cd cac mat la cac tam giac ddu. (a) Diing (b) Sai.
Cdu 57. Hinh chdp tam giac ddu cd cac mat la cac tam giac can. (a) Diing (b) Sai.
Cdu 58. Hinh chdp tii giac ddu cd day la hinh vudng.
(a) Diing (b) Sai.
Cdu 59. Hinh chdp tii giac ddu cd dudng cao la dudng ndi dinh va tam ciia day. (a) Dung (b) Sai.
Cdu 60. Hinh chdp tam giac ddu ed day la tam giac ddu.
(a) Diing (b) Sai.
Cdu 61. Hinh chdp tam giac ddu cd dudng ndi dinh va tam vudng gdc vdi day. (a) Diing (b) Sai.
72
Cdu 62. Cho hinh chdp SABCD, day ABCD la hinh vudng tam O. SA 1 (ABCD). SABCD la hinh chdp ddu.
(a) Diing (b) Sai.
Cdu 63. Cho hinh chdp SABCD, day ABCD la hinh vudng tam O. SO 1 (ABCD). SABCD la hmh chdp ddu.
(a) Diing (b) Sai.
Cdu 64. Cho hinh chdp SABCD, day ABCD la hinh vudng tam O. SA 1 (ABCD). SABCD khdng la hinh chdp ddu.
(a) Diing " (b) Sai.
H. DI£ N DUNG, SAI VAO 6 THICH HOP
Hdy dien dting, sai vdo cdc d trdng sau ddy md em cho Id hgp li nhdt. Cdu 65. Cho hinh chdp S.ABCD, day ABCD la hinh vudng canh a, SA = a SA l(ABCD).
(a) Thd tfch hinh chdp la a^
(b) Thd tfch hinh chdp la - a' 3
(c) Thd tfch hinh chdp la — a^ 6
(d) Ca ba cau trdn ddu sai. Trd ldi.
• D D D
a S
b S
c
d
D
S
73
Cdu 66. Cho hinh hop chit nhat ABCDA'B'CD' cd AA' = c, AB = a, AD - b B' a
y^\ D
' y^
y' B
(a) Thd tfch hinh hop la abc
(b) The tfch hinh chdp A'.ABCD la abc (c) Thd tfch hinh chdp A'.ABCD la - abc
(^) ^(ABCD.A'B'CD) ^ ^^(A'.ABCD ) Trd ldi.
D D D D
a
D
b S
c
D
d D
Cdu 67. Cho hmh hop chit nhat ABCDA'B'CD'. B'
C
A'
-' B
(a) Thd tfch hinh hdp la abc
(b) The tfch hinh chdp A'.ABD la abc • 74
(c) Thd tfch hinh chdp A'.ABD la - abc 6
(^)^(ABCD.A'B'C'D) =6^(A'.ABD) Trd ldi.
a
a D
b S
c
D
d D
Cdu 68. Cho hinh chdp S.ABCD, day ABCD la hinh vudng canh a, SA = a vudng gdc vdi day.
S
(a) SB = aV2
(b) SD = aV2
(c) Didn tfch tam giac SBD bang (d) Ca ba cau trdn ddu sai.
Trdldi.
a^Vi
n D D D
a D
b D
c
d
S
D
75
Cdu 69. Cho hinh chdp S.ABCD, day ABCD la hinh vudng eanh a, SA = a vudng gdc vdi day.
s
(a) SB = aV2
(b) SD = aV2
(c) Didn tfch tam giac SBD bing a^V3
(d) Thd tfch hinh chdp S.ABD bing Trd ldi.
D D n •
a D
b D
c
D
d
D
Cdu 70. Cho hinh chdp S.ABCD, day ABCD la hinh vudng canh a, SA = a vudng gdc vdi day.
S
76
(a) Dien tfch tam giac SBD bang a^Vs
(b) The tfch hinh chdp S.ABD bing — 6
(c) Khoang each tuf A ddn mp(SBD) la
(d) Ca ba eau trdn ddu sai.
Trd ldi.
2^
D •
D n
a D
b D
c
D
d S
Cdu 69. Cho hinh chdp SABCD, day ABCD la hinh vudng tam O, SA 1 (ABCD). S
((a) Tam giac SCD la tam giac vudng (b) Tam giac SCB la tam giac vudng (c) ASCD = ASBC
(d) Ca ba cau trdn ddu sai.
Trd ldi.
• • D D
a D
b D
c
D
d S
Cdu 71. Cho hinh lap phuong ABCDA'B'CD' canh a. B'
A
A' 1
)._ _ _ /'B
/
D'
/
/ /
/
(a) Thd tich khdi lap phuong la a'
1 3 (b) Thd tfch khdi chdp A'.ABCD la - a 3
1 (c) Thd tfch khdi lang tru ABDA'B'D' la -a^ 6
(d) Ca ba cau trdn ddu sai
Trd ldi.
D D
D D
a
D
b D
c
D
d S
Cdu 72. Cho hmh lap phuang ABCDA'B'CD' canh a.
B'
A A ;
/ B
C
/
D'
78
/
/ / /
(a) Thd tfch khdi lap phuong la a^
1 3 (b) The tfch khdi chdp A'.DD'C la - a 6
(c) Thd tfch khdi lang tm AA'B'.DD'C la -a^ 6
(d) Ca ba cau trdn ddu sai
Trd ldi.
0 D n 0
a D
b D
c
D
d S
///. CAU HOI DA WA CHON
Chgn cdu trd ldi ddng trong cdc bdi tap sau:
Cdu 73. Cho hinh chdp SABCD, day ABCD la hinh thang vudng tai A, SA l(ABCD), SA = a, AB = 2a, AD = DC = a. Khoang each tit C den (SAD) la
(a) a;
(c) a ^ ;
Trdldi (a).
Cdu 74. Cho hmh chdp SABCD, day ABCD la hinh thang vudng tai A, SA l(ABCD), SA - a, AB = 2a, AD = DC = a. Khoang each tii B ddn (SAD) la
79
D C
(a) a ; ^ (b) 2a
(c) aV3 ; (d)aV2.
Trd ldi (b).
Cdu 75. Cho hinh chdp SABCD, day ABCD la hinh thang vudng tai A,
SA l(ABCD), SA = a, AB = 2a, AD = DC = a. Khoang each tit A ddn (SBC) la s
(a) a;
(c) aV3 ;
Trd ldi. (d).
Cdu 76. Cho hinh chdp SABCD, day ABCD la hinh thang vudng tai A, SA l(ABCD), SA = a, AB = 2a, AD = DC = a. Khoang each tit B ddn (SAC) la
80
(a) a;
(c) aV2 ;
Trd ldi. (c).
Cdu 77. Cho hinh chdp SABCD, day ABCD la hinh thang vudng tai A, SA l(ABCD), SA = a, AB = 2a, AD = DC = a. Thd tfch khdi chdp la
(a)y (b)
(c)- ; (d) Ca ba cau trdn ddu sai.
Trd ldi. (a).
Cdu 73. Cho hinh chdp SABCD, day ABCD la hinh thang vudng tai A, SA J.(ABCD), SA = a, AB = 2a, AD = DC = a. Thd tfch khdi chdp S.ADC la
81
"""