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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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