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Kha hcLTHm bo mn Ton Thy L B Trn Phng Chuyn 01.Hnh hc khng gian

Hocmai.vnNgi trng chung ca hc tr Vit Tng i t vn: 1900 58-58-12 - Trang | 1 -

Lng trxin

Bi 1.

Cho hnh lng trABC.ABC c y l tam gic u cnh a, hnh chiu vung gc ca A ln mt phng(ABC) trng vi tm O ca tam gicABC. Tnh thtch khi lng trABC.ABC bit khong cch gia

AA v BC l3

4

a

Li gii:

Gi M l trung im BC ta thy:'

AM BC

A O BC

( ' )BC A AM

K ',MH AA (do A nhn nn H thuc trong on AA.)

Do

( ' )

( ' )

BC A AM

HM BCHM A AM

.

Vy HM l an vng gc chung ca AAv BC, do 3

( A',BC)4

d A HM a .

Xt 2 tam gic ng dng AAO v AMH, ta c:

'A O HM

AO AH

. 3 3 4'

3 4 3 3

AO HM a a aA O

AH a

Thtch khi lng tr:3

1 1 3 3' . ' . .

2 2 3 2 12ABC

a a aV A O S A O AM BC a

BI GING 05.

THTCH LNG TR (Phn 2)

HNG DN GII BI TP TLUYN

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Kha hcLTHm bo mn Ton Thy L B Trn Phng Chuyn 01.Hnh hc khng gian

Hocmai.vnNgi trng chung ca hc tr Vit Tng i t vn: 1900 58-58-12 - Trang | 2 -

Bi 2.

Cho hnh lng trtam gic u ABC.ABC c cnh y bng a. Bit khong cch gia hai ng thng

AB v AC bng15

5

a. Tnh thtch ca khi lng tr

Li gii:

Gi M; M ln lt l trung im ca AB v AB. H MH MC

AB // (ABC) ==> d(AB,AC) = MH

HC =15

10

a; MC =

15

2

a; MM = 3a

Vy V =33

4 a

Bi 3.Cho hnh lng trtam gic ABC.ABC vi A.ABC l hnh chp tam gic u cnh y AB = a; cnh

bn AA = b. Gi l gc gia hai mp(ABC) v mp(ABC). Tnh thtch chp A.BCCB.Li gii:

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Kha hcLTHm bo mn Ton Thy L B Trn Phng Chuyn 01.Hnh hc khng gian

Hocmai.vnNgi trng chung ca hc tr Vit Tng i t vn: 1900 58-58-12 - Trang | 3 -

Gi O l tm y suy ra 'A O ABC v gc 'AIA

'. ' ' . ' ' ' '.

2 2 2 2 2

1' . ' .

3

2 3 1 3 3. . .

3 2 2 63

A BCC B ABC A B C A ABC ABC ABCV V V A O S A O S

b a a a b aa dvtt

Bi 4.

Cho hnh hp ch nht ABCD.ABCD c AB=a, AB hp vi mt phng (ADCB) mt gc ,'BAC .

CMR :3

tan. ' ' ' ' sin( ) sin( )

cos cos

aABCD A B C DV

Li gii:

T A k ' ( ' ') ( ' ' )AH BA M CB ABB A CB AH AH A D CB

Suy ra : BH chnh l hnh chiu vung gc ca AB ln (ADCB) ABH

2 2

3

' AA ' tan a tan

( ' ') '. ' ' tan

' ' ' (tan tan )(tan tan )

sin( ) sin( )cos cos

tan. ' ' ' ' . . ' sin( ) sin( )

cos cos

ABA vu ng AB

AB BCC B AB BC ABC vu ng BC AB

BCC vu ng CB C B CC a

aCB

aABCD A B C D AB BC BBV

Gio vin: L B Trn Phng

Ngun: Hocmai.vn

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