vkt-phan ve co ban

8/3/2019 VKT-Phan Ve co ban

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BAI GIANG VE KY THUAT Trang 1

CHNG ICAC TIEU CHUAN TRNH BAY BAN VE

BAI 1 PHNG TIEN TRNH BAY BAN VE

I. VAT LIEU VE VA DUNG CU VE Vat lieu vela phng tien thc hien ban ve di dang tieu hao : Giay, but ch, gom,

Dung cu ve : la phng tien thc hien ban ve di dang tai s dung : thc

ke, eke, compa, rap ve vong tron,

II. CACH S DUNG CAC DUNG CU VE1. Van ve

Dung e thay the cho ban ve

chuyen dung. Khi s dung nen chon

mat that phang va canh trai that

thang. Giay c co nh ben goc trai

pha di cua van ve.

2. Thc TThc T c ket hp vi van ve e

dng cac ng bang. au thc T luon

ap sat vao van ve.

3. EkeDung e ket hp vi thc T e

dng cac ng thang ng hay cac

ng xien 30o, 45o, 60o.

4. Compa va rap vong tronCompa : dung e ve cac cung tron hay vong tron co ban knh ln.

Rap vong tron : dung e ve cac cung tron hay vong tron co ban knh nho.


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5. Gom (tay)Dung e tay, xoa cac vet d, cac net ve sai, tha tren ban ve. Trc khi dung

phai lau sach au gom.

6. But chNen chon but ch theo ky hieu cua ngoi ch. But ch mem (ky hieu B) dung e

ve cac netam, viet ch va so. But ch cng (ky hieu HB) dung e ve cac net manh.

Khi ve mui but ch phai ta vao canh tren cua thc va c xoay luc ve.

Nen dung but ch kim.

BAI 2 TIEU CHUAN TRNH BAY BAN VE

I. ng net (Theo TCVN 0008 1993 qui nh)

e bieu dien vat the, tren ban ve ky thuat dung cac loai net ve co hnh dang va

kch thc khac nhau. Cac loai net ve c qui nh theo TCVN.

Ten goi Hnh dang ng dung c ban

Net lien am

Be rong s

- Khung ban ve, khung ten.

- Canh thay, ng bao thay.

- ng nh ren thay, ng ren thay.

Net lien manh

Be rong s/3

- ng dong, ng dan, ng kch thc.

- ng gach gach tren mat.

- ng bao mat cat chap

- ng tam ngan.- ng than mui ten ch hng.

Net t

Be rong s/2

- Canh khuat, ng bao khuat.


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e n gian, ta dung ba kho ch sau :

Kho ch to (h7): ghi ta ban ve.

Kho trung bnh (h5): ghi ten hnh bieu dien, hng chieu, vet mat phang cat

Kho ch nho (h3.5): ghi so kch thc, yeu cau ky thuat, noi dung khung ten

va bang ke.

III.KHO GIAY (TCVN 2 74 qui nh)Kho giay la kch thc qui nh cua ban ve.

Theo TCVN kho giay c ky hieu bang 2 so lien

nhau.

Ky hieu theo TC ISO Ky hieu TCVN Kch thc

Kho giay 44 A0 1189 841

Kho giay 24 A1 594 841

Kho giay 22 A2 594 420

Kho giay 12 A3 297 420

Kho giay 11 A4 297 210

IV. KHUNG BAN VE VA KHUNG TEN

( TCVN 3821 83 qui nh)

Khung ban ve va khung ten ke bang net

lien am. Khung ban ve ke cach mep ngoaicua kho giay la 5mm. Trng hp muon ong

thanh tap th pha ben trai ke cach mep kho

giay la 25 mm. Khung ten at pha di goc

ben phai cua ban ve.


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Khung ban ve mau :

Trng Trung hoc KT - CN - NLp : THSCCK05A (6) (7)

(3)

(4)(2)Kiem tra

(1)Ngi ve

Ty le

(5)

- O

- 1 : Ho va ten ngi ve

- O2 : Ngi kiem tra ky ten- O3 : Ngay ve

- O4 : Ngay kiem tra

- O5 : Ten bai tap, ten chi tiet

- O6 : Ky hieu vat lieu

- O7 : Ky hieu bai tap

IV. TY LE (TCVN 3 74 qui nh)Ty le la ty so gia kch thc o c tren ban ve va kch thc tng ng o

c tren vat that. TCVN qui nh cac loai ty le sau :

Ty le nguyen hnh 1 : 1

Ty le phong to 2 : 1 2.5 : 1 4 : 1 5 : 1 10 : 1

Ty le thu nho 1 : 2 1 : 2.5 1 : 4 1 : 5 1 : 10

Chu y : Ty le cua ban ve ghi trong khung ten. Ty le cua hnh bieu dien ghi ben canh.


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BAI 3 GHI KCH THC

Kch thc ghi tren ban ve dung e cho biet o ln cua vat the. Theo TCVN5705 1993 qui nh.

I. QUI NH CHUNG Con so kch thc khong phu thuoc vao ty le ban ve va mc o chnh xac

cua ban ve.

n v kch thc dai la (mm) nhng khong ghi n v sau con so kch

thc.

n v : o, phut, giay phai ghi sau con so kch thc.

V DU :

II. CAC THANH PHAN CUA KCH THC1. ng dong

Ke bang net lien manh, vuong goc vi oan can ghi kch thc (trng hp

ac biet cho phep ke xien). ng dong vt qua ng ghi kch thc 3 5mm. Co

the dung ng tam keo dai lam ng dong.

2. ng kch thc

Ke bang net lien manh, song song vi oan can ghi kch thc, ng kch

thc cach oan can ghi kch thc t 5 10mm. Khong dung ng truc, ng

tam lam ng kch thc.

3. Mui tenMui ten at hai au ng kch thc, cham vao ng dong.


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Goc mui ten khoang 30o.

o ln cua mui ten ty le thuan vi be

rong cua net lien am. Neu ng

kch thc qua ngan th cho phep

thay mui ten bang net gach xien hay

dau cham.

4. Con so kch thcCon so kch thc ghi pha tren, khoang gia ng kch thc. Chieu cao

cua con so kch thc khongbe hn 3,5mm.

a. oi vi con so kch thc o dai : cac ch so c xep thanh hang song

song vi ng kch thc. Hng cua con so kch thc phu thuoc vao phng cua

ng kch thc.

ng kch thc nam ngang : con so kch thc ghi pha tren.

ng kch thc thang ng hay nghieng sang ben phai : con so kch thc

nam ben trai.

ng kch thc nghieng trai : con so kch

thc ghi ben phai.

ng kch thc nam trong vung gach gach :

con so kch thc c dong ra ngoai va at tren gia

ngang.

b. oi vi con so kch thc goc : hng vet cuacon so kch thc tuy thuoc vao phng cua ng vuonggoc vi ng phan giac o .

III.MOT SO QUI NH KHI GHI CAC LOAI KCH THC1. Kch thc song song : khi co nhieu kch

thc song song nhau th ghi kch thc nho trc, ln


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sau. Cac con so kch thc ghi so le nhau va khoang cach

eu nhau.

2. Ghi kch thc vong tron

3. Ghi kch thc cung tron

4. Ghi kch thc hnh vuong

IV. TRNH T THC HIEN BAN VE

1. Giai oan chuan b- Moi trng lam viec : sach, thoang mat, khong on.- Phng tien : ay u, hp ly.

2. Giai oan thc hien- Bo tr hnh ve tren giay

- Ve m


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- Ve am

- Ghi kch thc, noi dung khung ten.

- Ghi kch thc, noi dung khung ten.

3. Giai oan hoan chnh

- Kiem tra va sa lai ban ve.

CHNG 2VE HNH HOC

BAI 1 DNG HNH HOC

I. CAC NG THANG1. Dng ng trung trcCho oan thang AB, yeu cau dng ng trung trc

cua AB.

- Ve ng tron (A, R > AB/2)

- Ve ng tron (B, R)

- Hai ng tron nay cat nhau tai hai iem C va D.

- CD chnh la ng trung truc cua AB.

2. Dng ng vuong goca. Qua iem D nam ngoai ng thang (a)- Ve [D, R > d(D/a)], ng tron nay cat (a) tai

hai iem A va B.

- Dng ng trung truc cua oan thang AB.

- Nh vay DC chnh la oan thang can dng.

b. Qua iem D nam tren ng thang (a)


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- Dng (D, R), ng tron nay cat (a) tai hai iem

A va B.

- Dng ng trung trc cua oan AB.

- Nh vay, DC chnh la oan thang can dng.

c. Qua iem D nam au mut cua ng thang(a)

(Hoc sinh t dng)

3. Dng ng thang song song

Cho iem D nam ngoai ng thang (a).

Qua D hay dng ng thang song song vi (a).

II. VE CAC GOC

Goc phan giac Ve lai goc a cho Cac goc ac biet

III. O DOCo doc cua ng thang AB oi vi

ng thang AC la tg


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Goi o doc la i :AC

BCtgi ==

V du : ve o doc i = 1 : 6 cua ng thang i qua iem B oi vi ng thang

AC cho trc

IV. O CONo con ty so gia hieu ng knh hai mat cat vuong goc cua mot hnh non tron

xoay vi khoang cach gia hai mat cat o : tgh

dDk 2=

=

V du : ve hnh con nh A truc AB co o con : k = 1 : 5

V. CHIA EU NG TRON1. Chia ng tron lam 3 phan bang nhauCho (O, R = 2d), chia ng tron nay lam ba phan

bang nhau.

- Dng hai ng knh AB va CD vuong goc nhau.

- Ve ng tron tam (C, R). ng tron nay cat (O,

R) tai hai iem E va F.

- Nh vay, ba phan bang nhau cua ng tron (O, R) la ba cung DE, EF va FD.

2. Chia ng tron lam 5 phan bang nhau- Xac nh trung iem M cua oan AO.

- Dng ng tron tam M ban knh R=MC, ng

tron nay cat ng knh AB tai N.


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- CN chnh la canh cua hnh ngu giac noi tiep trong ng tron.

3. Chia ng tron lam 6 phan bang nhau(Hoc sinh t ve)

4. Chia ng tron lam 7, 9, 11, phan bang nhau- Dng (D, DC), ng tron nay cat AB keo dai tai E va F.

- Chia DC lam 7 oan thang bang nhau.

- Noi E va F vi cac iem chan.

- Cac ng thang nay keo dai cat ng tron tai cac iem G, H, I, K, L, M.

- Noi cac iem C, G, H, I, D, K, L, M lai ta co hnh can dng.


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BAI 2 VE NOI TIEP

I. VE TIEP TUYEN VI NG TRON1. Qua iem A tren ng tron

- Xac nh O oi xng vi O qua A

- Dng ng trung trc cua oan OO.

- AA chnh la tiep tuyen can dng.

2. Qua iem A ngoai ng tron- Xac nh trung iem M cua oan OA.

- Dng ng tron tam M, ng knh

OA, ng tron nay cat (O, R) tai 2

iem B va C.

- AB va AC chnh la tiep tuyen can dng.

II. TIEP TUYEN CHUNG CUA HAI NG TRON1. Tiep tuyen chung ngoai

Cho (O1, r va O2, R).

Yeu cau dng tiep tuyen chung cua hai ng tron nay.

r

O2

B2

O1

B1

M

BR-r

A1

A2

A R


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- Ve (O2, R-r).

- Dng tiep tuyen cua iem O1 oi vi (O2, R-r)

- O1A va O1B la hai tiep tuyen cua iem O1 oi vi (O2, R-r).

- O2A va O2B keo dai cat (O2, R) tai hai iem A1 va B1.

- Dng A1A2 song song vi O1A.

- Dng B1B2 song song vi O1A.

- A1A2 va B1B2 la tiep tuyen can dng

2. Tiep tuyen chung trong ( Hoc sinh t dng)

III. NOI HAI NG THANG BANG MOT CUNG TRON

IV. NOI NG THANG VI CUNG TRON BANG MOT CUNG TRON1. Tiep xuc ngoai

- Dng ng thang (d) song song va cach (d) mot khoang R.

- Dng ng tron (O, R + r), ng tron nay cat (d) tai O.

A1

B2

R

O1

A2

M

B1

B

O2

A

r

R+r


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- OO cat (O, r) tai iem 2.

- O-1 vuong goc vi (d).

- Cung tron tam tai O ban knh

R can dng i qua hai iem 1 va

2.

2. Tiep xuc trong (hoc sinh t ve)

V. NOI HAI CUNG TRON BANG MOT CUNG TRON KHAC


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1. Tiep xuc ngoai

- Ve ng tron (O, R + r).

- Ve ng tron (O, R +r).

- Hai ng tron nay cat nhau tai iem A.

- AO cat (O, r) tai B.

- AOcat (O, r) tai C.

- Cung tron (A, R) i qua hai iem B va C chnh la cung can dng.

2. Tiep xuc trong (Hoc sinh t ve)

3. Tiep xuc trong va ngoai (Hoc sinh t ve)


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BAI 3

DNG MOT SO NG CONG THONG DUNG

I. HNH O VANCho trc o dai hai truc AB va CD.

- Dng cung tron (O, OA), cung tron nay cat

CD keo dai tai E.

- Dng cung tron (C, CE), cung tron nay cat

AC tai M.

- Dng ng trung trc cua oan AM, ng

trung trc nay cat AB tai O1 va cat CD tai O2.

- Ve cung tron (O1, O1A), dng lai tai ng trung trc cua oan AM.

- Ve cung tron (O2, O2C), dng lai tai ng trung trc cua oan AM.

- Cung AC chnh la hnh can dng.

- Cac phan con lai hoc sinh t ve.

(Lu y : cac tam con lai lay oi xng qua O)II. HNH ELP

Elip la quy tch cua nhng iem co tong

khoang cach en hai iem co nh F1, F2 bang

mot hang so ln hn khoang cach gia hai iem

co nh.

V elip bit hai trc AB v CD

V hai ng trn tm O, ng knh l AB v CD. Chia 2 ng trn ra lm 12 phn u nhau T cc im chia 1, 2, 3...v 1', 2', 3'... k cc ng thng song song vi

trc AB v CD.

Giao im ca cc ng 1 1', 2 2' l cc im ni thnh Elip.


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V Elip khi bit 2 ng knh lin hp EF v GH* Phng php hai chm tia:

Qua E v F k MP v NQ // GH Qua G v H k PQ v MN // EF Chia cc on OH, PH, QH ra lm 3 phn bng nhau bi cc im 1, 2, 3 v

1',2', 3' (H l im chung 3 v 3' ca c 3 on ny) Ni E vi cc im 1', 2' thuc PH v vi 1, 2 thuc OH ; ni F vi cc im

1', 2' thuc HQ v 1, 2 thuc OH. Giao im ca 2 tia tng ng thuc 2 chm tia E v F xc nh cc im

thuc Elip.


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Phng php tm im

Qua A v B kng thng song song vi CD, qua C v D k hai ng

thng song song vi AB ta c hnh bnh hnh EFGH. Dng tam gic vung cn EIC (vung ti I). V cung trn tm C, bn knh CI ct ng thng EF ti K v L. Qua K v L v cc ng thng song song vi CD, cc ng thng ny

ct cc ng cho EG v HF ti 4 im 1,2, 3, 4 l nhng im thuc elipcn xc nh.

III. NG XOAN OC ARCHIMETng xoan oc Archimet la qui ao cua mot iem chuyen ong eu tren mot

ban knh quay khi ban knh nay quay eu quanh tam O.

o di cua iem tren ban knh quay nay

c mot vong goi la bc xoan.

Cac bc ve ng xoan oc Archimet

bc xoan a nh sau : Ve ng tron ban knh bang bc xoan

a va chia ng tron lam n phan bang nhau

Chia bc xoan a ra lam n phan bang nhau


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at len cac ng chia tai cac iem 1, 2, 3, cac oan thang 01, 02, 03,

c cac iem M1, M2, M3, thuoc ng xoan oc Archimet.

IV. NG THAN KHAI CUA NG TRONng than khai cua ng tron la quy ao cua mot iem thuoc ng thang

khi ng thang nay lan khong trt tren mot ng tron co nh (ng tron c s)

Ve ng than khai khi biet ng tron c s ban knh R.

Chia ng tron c s lam n phan bang nhau (v du n = 12)

Ve tiep tuyen cua ng

tron tai cac iem chia eu ng

tron

Lan lt at cac tiep tuyen tai

cac iem 1, 2, 3, cac oan thang bang

1, 2, 3, lan12

2R

, ta c cac iem

M1, M2, M3, thuoc ng than khai


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CHNG 3HNH CHIEU VUONG GOC

BAI 1 KHAI NIEM VE PHEP CHIEU

I. KHAI NIEM VE PHEP CHIEUTrong khong gian cho mat phang (P) va mot

iem S co nh ngoai mat phang (P). T mot iem

A bat ky trong khong gian dng ng thang SA.

ng thang nay cat (P) tai A. Ta noi rang a thc

hien phep chieu iem A len mat phang (P). S : tam chieu

A : vat chieu

(P) : mat phang hnh chieu

SA : tia chieu

A : hnh chieu cua A

II. PHAN LOAI PHEP CHIEU1. Phep chieu xuyen tamLa phep chieu ma cac tia chieu ong qui tai

mot iem S co nh. iem S goi la tam chieu.

A, B, C : goi la hnh chieu xuyen tam cua A,

B, C tren mat phang (P), tam chieu S.

2. Phep chieu song songPhep chieu song song la phep ma cac tia chieu song song vi mot ng

thang (a) co nh, ng thang nay goi la phng chieu.

Qua iem A dng ng thang song song vi (a). ng thang nay cat (P) tai

A. A goi la hnh chieu song song cua A tren (P) theo phng chieu (a).

P

A'

A

S

C

B'

P C'

A'

B A

S


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Phep chieu song song c chia lam hai loai :

Phep chieu xien : la phep chieu ma phng chieu nghieng so vi mat

phang hnh chieu.

Phep chieu vuong goc : La phep chieu ma phng chieu vuong goc vi

mat phang hnh chieu.

Cac tnh chat cua phep chieu song song :

Hnh chieu cua ng thang song song van la

cac ng thang song song : AB // CD AB // CD

Ty so cua cac oan thang song song van

c gi nguyen khi chieu :

''

''//

DC

BA

CD

ABCDAB =

Ty so n cua 3 iem thang hang cung c gi nguyen.

( ) ( )'''''

''EBA

EB

EA

BE

AEABE ===

III. PHNG PHAP VE CAC HNH CHIEU VUONG GOCTa thay rang, mot iem A trong khong gian th co mot hnh chieu duy nhat tren

mat phang hnh chieu la A. Nhng ngc lai, t mot hnh chieu A ta lai co the xac

nh c vo so cac iem khac nhau A, B, C, tren cung mot hnh chieu. Suy ra,

biet mot hnh chieu cua vat the tren mot mat phang hnh chieu th ta cha the hnh

PA'

A(a)

PHEP CHIEU VUONG GOC PHEP CHIEU XIEN

PA'

(a)

A


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dung c vat the o trong khong gian. Do vay, e tranh nham lan can phai co hai

hnh chieu tr len.

Phng phap ve hnh chieu vuong goc cua vat the :

Chieu vuong goc vat the len cac mat phang hnh chieu vuong goc nhau tng oi

mot. Sau o xoay cac mat phang hnh chieu trung nhau thanh mot mat phang (xoay

theo qui c). Mat nay chnh la mat phang ban ve. Luc nay tren mat phang cua ban

ve se co nhieu hnh chieu vuong goc cua vat the. Nghien cu cac hnh ve nay ta se

hnh dung ra hnh dang cua vat the trong khong gian


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BAI 2

HNH CHIEU CUA IEM OAN THANG HNH PHANG

I. HNH CHIEU CUA IEM1. Hnh chieu cua iem tren hai mat phang

Trong khong gian cho iem A tuy y va hai mat phang (P1), (P2) vuong goc nhau

theo giao tuyen x.

T A dng ng thang vuong goc vi (P1) va (P2), ta co A1 va A2 tren hai mat

phang (P1) va (P2).

A1 : hnh chieu ng cua A

A2 : hnh chieu bang cua A

A1A2 : ng dong

P1 : mat phang hnh chieu ng

P2 : mat phang hnh chieu bang

AA1 = A2Ax : o xa cua A

AA2 = A1Ax : o cao cua A

Quay (P2) quanh x mot goc 90o theo chieu nh hnh ve, ta co P2 P1. Khi o

A1A2 Ax. A1A2 con goi la o thc cua A tren hai mat phang.

A

A1

AX

A2

Ox

P2

P1 P1

P2

A1

AX

A2

x

A2

AX

A1

x


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2. Hnh chieu cua iem tren ba mat phangTrong khong gian cho iem A va 3 mat phang P1, P2, P3 vuong goc nhau theo

giao tuyen Ox, Oy, Oz

A3 : hnh chieu canh

AA3 = AzAy : o xa hnh chieu canh

Quay mat phang P3 va P2 trung vi mat phang P1, ta co o thc cua iem tren ba

mat phang.

II. HNH CHIEU CUA OAN THANG

oan thang c xac nh bi hai iem bat ky.

1. o thc cua oan thang

2. o thc cua oan thang v tr ac bietng thang song song vi MPHC nao th hnh chieu cua ng thang tren mat

phang o la chnh no.

A

A1

AX

A2

Ox

P2

P1 P1

P2

A1

AX

A2

xA3

AZ

Ay

z

y

O

Ay

AZ A3

z

y

AX

A2 y Ay

O

A3AZ

z

A1

x

P3

P3

A

A1

AX

A2

Ox

P2

P1

A3

AZ

Ay

z

y

AX

A2 Ay

O

A3AZA1

x

P3

BX

B1

B B3

By

B2

BZB1

ByB2

B3BZz

yBX


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2.1. ng thang song song vi MPHC

2.1.1. ng mat : ng thang song song vi MPHC

2.1.2. ng bang : ng thang song song vi MPHCB

Nhan xet : Hnh chieu ng song song vi truc x

2.1.3. ng canh : ng thang song song vi MPHCC

P1 z

x

P2 y

P3

Ox

z

y

yAB

B1

A1

A2 B2

B3

A3

B1

A1

A2 B2

B3

A3

P1 z

x

P2 y

P3O x

z

y

yAB

B1A1

A2 B2

B3

A3

B1A1

A2

B2

B3 A3

P1z

x

P2 y

P3

O x

z

y

yA

B

B1

A1

A2B2

B3

A3

B1

A1

A2

B2

B3

A3


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2.2.ng thang vuong goc vi MPHCng thang vuong goc vi MPHC nao th hnh chieu cua no tren mat phang o

la mot iem.

2.2.1. ng thang tia chieu ng : AB MPHC

2.2.2. ng thang tia chieu bang : AB MPHC

2.2.3. ng thang tia chieu canh : AB MPHCC

P1z

P3

yP2

xO

z

xyB

A A3

B3A2

B2

A1 B1A1 B1

A2

B2

A3 B3

O

z

x

P1

A2 B2

B1

B

A1

A

P3

O

A3B3

A3

A2 B2

B1

x

A1

O

z

y

yP2 y

B3

P1

x

P2 yP3

O

y

xy

z

O

A1 B1

A B

A2 B2

A3B

3

A1 B1

A2 B2

A3 B3


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III. HNH CHIEU CUA MAT PHANG

1. Cach xac nh mat phang trong khong gianQua 3 iem khong

thang hang

Mot iem nam

ngoai mat phang

Hai ng thang

cat nhau

Hai ng thang

song song

2. o thc cua mat phangTrong khong gian cho 3 iem phan biet A, B, C va ba mat phang P1, P2, P3

vuong goc nhau theo giao tuyen Ox, Oy, Oz.

A1BZ

A1

AXxO

A2P2

B2

BXA

B

AZ

y

ByAy

B3

A3P3

A2

B2

AXx

BX

P1B1

z zB1

AZA3

ByAy

O y

BZ B3

C1

C3C

C1

C2C2

C3CZ

Cy

3. o thc cua mat phang nhng v tr ac biet3.1.Mat phang vuong goc vi MPHCMat phang vuong goc vi mat phang hnh chieu th hnh chieu cua no suy bien

thanh mot oan thang.


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3.1.1.Mat phang chieu ng

- A, B, C thuoc mat phang (Q).

- (Q) (P1).

- Chieu A, B, C len (P1), (P2), (P3).

3.1.2.Mat phang chieu bang

3.1.3.Mat phang chieu canh

P1

x

P2 yP3

Ox

y

z

O

A1

B1

A2B2

A2

B2C2

A

B

C

C2

A3

B3

C1 C3

Q


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3.2.Mat phang song song vi MPHCMat phang song song vi MPHC nao th hnh chieu cua no tren mat phang

o la chnh no.

3.2.1. Mat phang bang : mat phang song song vi MPHCB

3.2.2. Mat phang ng (Mat phang mat) : mat phang song song vi MPHC

3.2.3. Mat phang canh : Mat phang song song vi MPHCC


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BAI 3 HNH CHIEU CUA CAC KHOI HNH HOC

I. KHOI A DIENKhoi a dien la khoi hnh hoc c gii han bang cac a giac phang. Cac a giac

phang c goi la cac mat cua khoi a dien, cac nh va cac canh c goi la nh

va canh cua khoi a dien.

Cac a dien thng gap : khoi lang tru, khoi thap, khoi thap cut.

3. Khoi lang tru : la khoi a dien co cac canh ben song song

Khoi lang tru ng : canh ben

vuong goc vi MPHC.

Khoi lang tru xien : canh ben

khong vuong goc vi MPHC

4. Khoi thap : la khoi a dien co cac canh ben ong qui.

Khoi thap ng : cac canh

ben bang nhau

Khoi thap xien : cac canh

ben khong bang nhau.

II. KHOI TRONLa khoi hnh hoc gii han bi mat tron xoay : khoi cau, khoi xuyen hay gii han

bi mot phan mat tron xoay va mat phang (mat tru, mat non, na cau, ). Mat tron

xoay tao bi mot ng thang bat ky quay quanh mot truc co nh. ng bat ky o

goi la ng sinh cua mat tron xoay. Truc co nh goi la truc quay cua mat tron

xoay.

KHOI LANG TRU XIENKHOI LANG TRU NG

KHOI LANG TRU XIENKHOI LANG TRU NG

S

O

BA

D C

S

A B

CD

O


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Mat tru tron xoay : ng sinh song song vi truc quay.

Mat non tron xoay : ng sinh cat truc quay

Neu ng sinh la na ng tron (hoac ng tron) quay quanh truc vi

ieu kien mat phang cha ng tron va truc i qua tam cua ng tron se

tao mat cau.

Neu truc quay thuoc mat phang cha ng tron nhng khong i qua tam

cua ng tron tao thanh mat xuyen.


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III. BIEU DIEN HNH CHIEU CUA CAC KHOI HNH HOC C BAN

Khi dng o thc cac khoi hnh hoc c ban theo cac v tr sau e

at cac khoi goc 1/8 th nhat.

Neu khoi hnh hoc co truc oi xng hay truc quay th nen at truc thang goc

hay song song vi mot MPHC.

1. Khoi hnh hop

2. Khoi lang tru ay tam giac

3. Khoi lang tru ay luc giac eu

4. Hnh chieu cua hnh chop ng4.1.Hnh chop ng ay vuong


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4.2. Hnh chieu cua chop xien

5. Hnh tru

6. Hnh non


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7. Hnh cau

BAI 4 GIAO TREN BE MAT VI CAC KHOI HNH HOC

I. GIAO TUYEN CUA MAT PHANG VI KHOI A DIEN

1. Giao tuyen cua mat phang vi khoi a dienGiao tuyen cua mat phang vi khoi a dien la mot hnh a giac.

2. Giao tuyen cua matphang vi hnh tru

1.1. Mat phang vuong goc vi hnh tru : giao tuyen la mot ng tron

1.2. Mat phang nghieng vi truc cua hnh tru : Giao tuyen la mot hnh elp


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1.3. Mat phang song song vi truc cua

hnh tru : Giao

tuyen la hnh ch

nhat.

II. GIAO TUYEN CUA CAC KHOI HNH HOC

3. Giao tuyen cua cac khoi a dienKhoi a dien c gii han bi cac a giac

nen giao tuyen cua hai khoi a dien la ng

gay khuc khep kn.

4. Giao tuyen cua hai khoi truGiao tuyen cua hai khoi tron la mot

ng cong khong gian khep kn. Muon ve giao

tuyen cua khoi tron, ta tm mot so iem cua

giao tuyen roi noi lai.2.1. Giao tuyen cua hai hnh tru co truc vuong goc

Hai khoi tru co ng knh khac nhau Hai khoi tru co ng knh bang nhau


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5. Giao tuyen cua hnh tru vi hnh cau va hnh non vi hnh cau

III. GIAO TUYEN CUA KHOI A DIEN VI KHOI TRON

Giao tuyen cua khoi a dien vi khoi tron la giao tuyen cua cac mat a dien vi

cac mat cua khoi tron.


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Neu hnh chieu th ba oi xng : chon truc oi xng lam truc.

Hnh chieu th ba khong oi xng : chon ng bao bien lam chuan.

Cac kch thc o c t hnh chieu bang a ra hnh chieu canh.

(Co the dung ng thang nghieng 45o lam ng phu tr e ve hnh chieu th ba).

CHNG IV HNH CHIEU TRUC O

BAI 1. KHAI NIEM VE HNH CHIEU TRUC O

1. Khai niemHnh chieu truc o : La hnh bieu dien

cua vat the c dng t mot he truc o.

He truc o : La hnh chieu cua mot he

gom 3 truc vuong goc xac nh 3 chieu kchthc, thc hien bi phep chieu song song va

c goi la phep chieu truc o.

Hnh chieu truc o c xac nh theo

phng chieu va he so bien dang cua cac truc.

2. Phan loai hnh chieu truc o.a. Phan loai hnh chieu truc o theo phng chieu : Hnh chieu truc o xien : Phng chieu v tr bat ky oi vi mat phang

hnh chieu.

Hnh chieu truc o vuong goc : Phng chieu vuong goc vi mat phang

hnh chieu.

Po

X'

Y'

Z'

Z

XYO

O'

A

AB

C

A'

B'

C'


41/58


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BAI 2 CAC LOAI HNH CHIEU TRUC O

Co hai loai hnh chieu truc o tieu chuan va thng dung :

Hnh chieu truc o vuong goc eu.

Hnh chieu truc o xien ng can.

1. Hnh chieu truc o vuong goc eua. Khai niem :

Hnh chieu truc o vuong goc eu : La loai hnh chieu truc o co phng

chieu vuong goc vi mat phang hnh chieu.

b. Quy c :Tieu chuan nha nc quy nh v tr va he so bien dang cua he truc o vuong

goc eu nh sau :

Truc ng : (Oz)

Hai truc nghieng (Ox, Oy) mot goc 30o oi vi ng bang.

He so bien dang : Kx = p = 1 ; Ky = q = 1 ; Kz = r = 1

Chu y : Hnh phang nam trong hoac song song vi cac mat phang truc toa oeu ve bien dang tren hnh chieu truc o vuong goc eu.


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Cach ve hnh o van nh hnh ve :

Biet :

Truc ln cua hnh o van : 1,22d

Truc nho cua hnh ovan : 0.7d

2. Hnh chieu truc o xien ng canHnh chieu truc o xien ng can : La loai hnh chieu truc o co phng chieu

khong vuong goc vi mat phang hnh chieu (P).

Tieu chuan nha nc quy nh : V tr va he so bien dang cua he truc o xien

ng can nh sau :

Truc ng (Oz).

Truc ngang (Ox)

Truc nghieng (Oy) vi goc 45o oi vi ng bang.

Kx

= p = 1 ; Ky

= q = 0.5 ; Kz

= r = 1

Hnh phang nam trong hoac song song vi mat phang (Ox, Oz) se khong b

bien dang tren hnh chieu truc o xien ng can.


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BAI 3 CACH DNG HNH CHIEU TRUC O

1. Phng phap toa oPhng phap toa o : la phng phap c ban e dng hnh chieu truc o cua

vat the.

Tuy nhien, muon dng hnh chieu truc o cua vat the ta phai dng c hnh

chieu truc o cua mot iem.

Cach dng hnh chieu truc o cua mot iem nh sau :

Trc het ve v tr cac truc o cua he truc o va xac nh toa o vuong goc cua

iem A (XA, YA, ZA), sau o can c vao he so bien dang cua cac truc o ma xac nh

toa o truc o cua iem o vi :

XA = p3 XA ; YA = q3 YA ; Z = r3 ZA

Lan lt at cac toa o truc o len cac he truc o ta se xac nh c iem

A la hnh chieu truc o cua iem A.

2.ac iem ve cach dnga. Vat the co dang hnh hop : Ta ve hnh hop ngoai tiep cho vat the va chon 3

mat cua hnh hop lam 3 mat phang toa o.

b. Vat the co mat oi xng : Ta nen chon mat phang oi xng lam mat phangtoa o.


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CHNG VHNH BIEU DIEN CUA VAT THE

BAI 1 HNH CHIEU

1. Khai niemHnh chieu : la hnh bieu dien cac phan

thay cua vat the oi vi ngi quan sat .

Cho phep the hien cac phan khuat cua vat

the bang net t e giam so lng ve hnh

bieu dien.

2. Phng phap bieu diene cu the hoa cach bieu dien, nha nc quy nh dung 6 mat cua hop lap

phng lam 6 mat phang chieu c ban. Hop lap phng nay goi la hop hnh

chieu. Cac mat (2), (3), (4) , (5), (6) co the m va trai phang ra trung vi mat (1) nh

hnh ve :


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3. Phan loaia. Hnh chieu c ban

Hnh chieu c ban la hnh chieu cua cac vat the tren cac mat phang hnh chieu

c ban cua hop hnh chieu.

Hnh chieu c ban co ten goi la :

Hnh chieu t trc (Hnh chieu ng hay hnh chieu chnh).

Hnh chieu t tren (Hnh chieu bang).

Hnh chieu t trai (Hnh chieu canh).

Hnh chieu t phai.

Hnh chieu t di.

Hnh chieu t sau.

Hnh chieu t trc con goi la hnh chieu

chnh, hnh chieu nay c chon sao cho phan

anh ac trng hnh dang cua vat the. Cac hnh

chieu khac phai ung v tr oi vi hnh chieu t

trcnhng neu cac hnh chieu nay khong ungv tr hoac b phan cach bi mot hnh bieu dien

khac th phai c ch danh bang ch hoa va ch

hng bang mui ten nh hnh ve tren.

b. Hnh chieu rieng phan- Hnh chieu rieng phan : La hnh

chieu mot phan cua vat the tren matphang hnh chieu song song vi mat

phang hnh chieu c ban.

- Hnh chieu rieng phan phai cch danh va ch hng neu khong ve

A

A


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ung v tr chieu .

c. Hnh chieu phu- Hnh chieu phu la hnh chieu mot

phan cua vat the tren mat phang hnh

chieu khong song song vi mat phang hnh

chieu c ban.

- Hnh chieu phu nen at ung v tr chieu.Neu khong th phai ch danh va ch hng.

- e thuan tien cho viec bo tr tren banve, tieu chuan nha nc cho phep ve xoay

hnh ve v tr thch hp. Trong trng hp

nay hnh bieu dien phai c k hieu bang mui ten cong.

BAI 2 HNH CAT

oi vi nhng vat the co cau tao ben trong phc tap, neu ch dung hnh

chieu e bieu dien th hnh ve co nhieu ng khuat, nh the ban ve se khongro rang. e khac phuc ban ve ky thuat dung hnh cat va mat cat e bieu diencau tao ben trong cua vat the

1. Khai niemHnh cat : La hnh bieu dien phan con lai cua vat the sau khi a tng tng cat

i phan vat the gia mat phang cat va ngi quan sat.

2. Phng phap bieu dienVat the c cat bi mot hay nhieu mat phang goi la mat phang cat. Chieu phan

vat the nam gia mat phang cat va mat phang hnh chieu ta se co hnh cat. Do vay

hnh cat c xem la hnh chieu cua mot phan vat the ( gia mat phang cat va mat

phang hnh chieu) tren mat phang hnh chieu.


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Chu y :

Vat the c tng tng b cat e ve hnh cat nhng thc te khong b cat

nen cac hnh chieu khac phai c gi nguyen.

e phan biet hnh cat vi cac hnh chieu th hnh cat phai c ch danh bang

ch hoa va c k hieu vat lieu tren dien tch b cat, ong thi phai xac nh vet mat

phang cat bang net cat co ch danh va ch hng bang ch hoa tren hnh chieu.

ng gach gach (ng tuyen anh) : La nhng ng net lien manh dung

e k hieu vat lieu mat cat cua vat the, co khoang cach t 3 5mm vi o nghieng

45o oi vi ng bang, ng bao hay ng truc chnh cua hnh ve. Neu can co

the chon o nghieng 30o hoac 60o

1 2

3

P

A

A

A - A


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ng gach gach phai thong nhat o nghieng va khoang cach tren cung

dien tch cat cua vat the.

ng gach gach phai khac o nghieng va khoang cach tren vung dien tch

cat cua hai vat the.

ng gach gach co the c gian lc theo chu vi ng bao neu dien

tch cat qua rong.

ng gach gach c thay bang boi en neu dien tch cat qua hep.

3. Phan loai hnh cata. Phan loai hnh cat theo v tr mat phang Hnh cat ng : Mat phang cat song song vi MPHC

Hnh cat bang : Mat phang cat song song vi MPHCB


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Hnh cat canh : Mat phang cat song song vi mat MPHCC.

Hnh cat nghieng : Mat phang chieu v tr bat ky. e tien bo tr hnh

tren ban ve, ta co the ve xoay hnh cat nghieng v tr thch hp va c ky hieu

bang mui ten cong tren hnh ve

Hnh cat ng, bang, canh, nhieng : La nhng hnh bieu dien c ve ung v

tr thay cho hnh chieu t trc, hnh chieu t tren (hoac hnh chieu t di), hnh

chieu t trai ( hoac hnh chieu t phai ), hnh chieu phu.

4. Phan loai hnh cat theo so lng mat phang cat Hnh cat n gian : La hnh cat ch co mot mat phang chieu. Hnh cat n

gian co dang la hnh cat doc hoac hnh cat ngang.

Hnh cat phc tap :

La do hai hay nhieu mat phang chieu. Hnh cat phc tap co dang la hnh cat

bac ( do ket hp bi 2 hay nhieu mat phang chieu ong qui ),

a. Hnh cat bac : Cac MPC song song nhau (dang bac thang)b. Hnh cat xoay : Cac MPC giao nhau hp thanh goc tu.


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AA

A

A - A

A

A

A - A

5. Cac hnh cat ac biet Hnh cat rieng phan : Hnh cat rieng phan la

hnh cat mot phan nho cua vat the. Hnh cat nay at taingay v tr tng ng tren hnh chieu c ban . ng gach

gach c gii han bang net ln song. Khong can ch

danh va ch hng tren hnh cat.

Hnh chieu ket hp hnh cat : dung e dien ta hnh dang ben trong lan ben

ngoai cua vat tren mot hnh bieu dien. (Muc ch la giam bt so lng hnh bieu dien)

Neu hnh chieu va hnh cat co chung truc oi xng th ghep chung vi nhau,lay tam lam ng phan cach.

Net t (ng bao khuat) phan hnh chieu oi xng vi net am (ng bao

thay) phan hnh cat th boi i.

Neu net am trung vi ng tam th dung net ln song lam ng phan

cach (the hien net am).


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Neu hnh chieu va hnh cat khong co truc oi xng th dung net ln song lam

ng phan cach.

6. Nhng phan khong ve ky hieu vat lieu tren mat cata. Cac chi tiet nh : vt, bulong, inh tan, then, truc ac, qui c khong b cat

theo be doc. Cac vien bi cung qui c khong b cat.b. Mot so phan t cua chi tiet may nh : nan hoa cua vo lang, gan lc, rang

cua banh rang, qui c khong ky hieu vat lieu tren mat cat cua chung khi cat theo

be doc.

Bai 3 MAT CAT

Mat cat dung e the hien hnh dang va cau tao

phan t b cat ma tren cac hnh chieu kho the hien

c.


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1. Khai niemMat cat la hnh bieu dien nhan c tren MPC khi ta tng tng dung mat cat

nay cat vat the.

Hnh cat Mat cat

B

B

B - B

B

B

B - B

2. Phan loai2.1.Mat cat ri : dung e the hien nhng phan t co ng bao MC phc tap.Mat cat ri at ngoai hnh bieu dien tng ng (co the at gia hnh phan cat

la cua mot hnh bieu dien nao o). ng bao cua MC ri ve bang net lien am.

Mat cat ri c at doc theo ng keo dai cua net cat va at gan hnh bieu

dien tng ng ( cho phep at tuy y)..

2.2.Mat cat chapMat cat chap at ngay tren hnh bieu dien

tng ng. ng bao cua mat cat chap ve

bang net lien manh. Cac ng bao tai cho

at mat cat chap van gi nguyen.


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3. Ky hieu va qui nh ve mat cata. Tren mat cat cung ghi ky hieu giong hnh cat (vet cat, ch hng bang mui ten

va ch danh bang ch hoa).

b. Neu mat phang cat la hnh oi xng ma truc oi xng trung vi vet mat cat

hay trung vi ng keo dai cua mat cat th khong can ghi chu.

c. Neu mat cat chap, mat cat ri khong phai la hnh oi xng th ch ve net cat va

mui ten ma khong can ch danh. (Nh mui ten, ta mi biet phan t nao pha trc).

Neu mat cat qua cac lo hoac phan lom dang tron xoay

th ng bao cua lo hay lom o c ve ay u tren mat

cat. Qui c nay giup ngi oc ban ve phan biet c

cac lo, cho lom tron xoay, ranh khong tron xoay.

d. Neu cac mat cat giong nhau ong thi de xac

nh v tr cac mat cat o hnh bieu dien th cho phep

ch ve net cat cua mot mat cat, ong thi ghi ro so

lng cua cac mat cat o.

B

B

B - B

C

C

C - C

B

B

B

B


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e. Cho phep ve xoay mat cat e tien bo tr tren ban ve. Trong trng hp nay

hnh ve phai c ky hieu bang mui ten cong.

BAI 4 HNH TRCH

1. Khai niemHnh trch : La loai hnh bieu dien thng c phong to trch t hnh bieu dien

chnh nham the hien ro ket cau qua nho cua vat the

2. Phng phap bieu diene ch dan phan c trch t hnh bieu dien chnh, tieu chuan nha nc qui nh

dung net lien manh khoanh vung c trch ( bang vong tron hoac elip) kem theo so

th t La ma tng ng va t le phong to.

3. Qui nh ve hnh trcha. Nen at hnh trch gan v tr khoanh vung trch.

b. Hnh trch bao gom ca nhng van e cha the hien tren hnh bieu dien chnh

va cung co the la loai hnh bieu dien khac vi hnh bieu dien chnh.

R

I

TL 2:1

R

TL 2:1

III II


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MUC LUC

CHNG 1 CAC TIEU CHUAN TRNH BAY BAN VEBAI 1 PHNG TIEN TRNH BAY BAN VE

I. Vat lieu ve va dung cu ve .............................................................................. 1II. Cach s dung cac dung cu ve ...................................................................... 1

BAI 2 TIEU CHUAN TRNH BAY BAN VEI. ng net .................................................................................................... 2II. Ch va so ..................................................................................................... 3III. Kho giay ....................................................................................................... 4IV. Khung ban ve va khung ten ......................................................................... 5V. Ty le ............................................................................................................ 5

BAI 3 CHI KCH THCI. Quy nh chung ............................................................................................ 6II. Cac thanh phan cua kch thc ................................................................... 6III. Mot so quy nh khi ghi kch thc ............................................................... 7IV. Trnh t thc hien ban ve ............................................................................. 8

CHNG 2 VE HNH HOCBAI 1 DNG HNH HOC

I. Dng cac ng thang ................................................................................. 9II. Ve cac goc .................................................................................................. 10

III. o doc ......................................................................................................... 11IV. o con ......................................................................................................... 11V. Chia ng tron thanh cac phan bang nhau ............................................... 11

BAI 2 VE NOI TIEPI. Ve tiep tuyen vi ng tron ....................................................................... 13II. Tiep tuyen chung cua hai ng tron .......................................................... 13III. Noi hai ng thang bang mot cung tron .................................................... 14IV. Noi ng thang vi cung tron bang mot cung tron .................................... 14

V. Noi hai cung tron bang mot cung tron khac ................................................ 15BAI 3 DNG MOT SO NG CONG THONG DUNG

I. Hnh ovan ..................................................................................................... 17II. Hnh elip ....................................................................................................... 17III. ng xoan oc archimet .............................................................................. 18

IV. ng than khai cua ng tron ................................................................. 18CHNG 3 HNH CHIEU VUONG GOCBAI 1 KHAI NIEM VE PHEP CHIEU

I. Khai niem ve phep chieu ............................................................................. 19II. Phan loai phep chieu ................................................................................... 19III. Phng phap ve cac hnh chieu vuong goc ................................................. 20

BAI 2 HNH CHIEU CUA IEM OAN THANG HNH PHANGI. Hnh chieu cua iem .................................................................................... 22


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II. Hnh chieu cua oan thang .......................................................................... 23III. Hnh chieu cua mat phang ........................................................................... 26

BAI 3 HNH CHIEU CUA CAC KHOI HNH HOCI. Khoi a dien ................................................................................................. 29II. Khoi tron ...................................................................................................... 29III. Bieu dien hnh chieu cac khoi hnh hoc c ban ............................................ 31

BAI 4 GIAO TUYEN TREN BE MAT VI CAC KHOI HNH HOCI. Giao tuyen cua mat phang vi khoi a dien ................................................ 33II. Giao tuyen cua cac khoi hnh hoc ............................................................... 34III. Giao tuyen cua khoi a dien vi khoi tron ................................................... 35

BAI 5 BIEU DIEN VAT THE1. Cach phan tch vat the thanh cac khoi hnh hoc c ban ............................. 352.. Cach ve hnh chieu th ba t hai hnh chieu a cho .................................. 36

CHNG IV HNH CHIEU TRUC OBAI 1 KHAI NIEM VE HNH CHIEU TRUC O

1. Khai niem ................................................................................................... 372.. Phan loai hnh chieu truc o ...................................................................... 37

BAI 2 CAC LOAI HNH CHIEU TRUC O1. Hnh chieu truc o vuong goc eu .............................................................. 382.. Hnh chieu truc o xien ng can ............................................................... 39

BAI 3 CACH DNG HNH CHIEU TRUC O1. Phng phap toa o .................................................................................... 402. ac iem ve cach dng .............................................................................. 40

CHNG V HNH BIEU DIEN CUA VAT THEBAI 1 HNH CHIEU

1. Khai niem .................................................................................................... 422.. Phng phap bieu dien ............................................................................... 423. Phan loai ..................................................................................................... 43

BAI 2 HNH CAT1. Khai niem .................................................................................................... 442.. Phng phap bieu dien .............................................................................. 443. Phan loai hnh cat ...................................................................................... 46

BAI 3 MAT CAT1. Khai niem ................................................................................................... 50

2.. Phan loai .................................................................................................... 503. Ky hieu va quy nh ve mat cat .................................................................. 50BAI 4 HNH TRCH

1 Kh i i 2

vkt-phan ve co ban

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