Distante in cub clasa 8
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Transcript of Distante in cub clasa 8
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Distanțe în cub
Fie cubul ABCDA’B’C’D’ de latură a. Aflați: a) d(A’; D); b)
d(A;BB’);d(A’;CC’);d(C;AC’);d(A’;BD); c) d(D’; (ABC)); d(A; (A’BD)); d) d(A’D’;AD); d(A’D’;BC); d(A’D;
B’C); e) d(A’B’; (DCC’)); f) d((A’AD); (B’C’C)).
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1.a)
d(A’; D) = ?
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1.a)
d(A’; D) = A’D =
2aa2aa 222
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1.b1)
d(A; BB’) = ?
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1.b1)
AB BB’ => d(A; BB’) = AB = a
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1.b2)
d(A’; CC’) = ?
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1.b2)
d(A’; CC’) = A’C’
CC’ (A’B’C’), A’C’ (A’B’C’) => CC’ A’C’
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1.b2)
d(A’; CC’) = A’C’ = a
A’B’C’, (m<(B’) = 90o) => A’C’ = a
2
2
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1.b3)
d(C; AC’) = ?
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1.b3)
CE AC’ => d(C; AC’) = CE
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1.b3)
CE = hACC’; ACC’ = dreptunghic
d(C; AC’) = CE = (AC . CC’)/AC’ =
36a
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1.b4)
d(A’; BD) = ?
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1.b4)
A’O DB => d(A’; DB) = A’O
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1.b4)
DB=A’D=A’B= d(A’;BD) = A’O = hA’BD
= 26a
2a => A’BD = echilateral
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1.c1)
d(D’; (ABC)) = ?
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1.c1)
D’D (ABC) => d(D’; (ABC)) = D’D = a
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1.c2)
d(A; (A’BD)) = ?
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1.c2)
AH (A’BD) => d(A; (A’BD)) = AH
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1.c2)
AH = hA’AO; A’AO = dreptunghic
d(A; (A’BD)) = AH = (AO . AA’)/OA’ =
33a
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1.d1)
d(A’D’; AD) = ?
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1.d1)
A’D’ AD; AA’ AD; AA’ A’D’
d(A’D’; AD) = AA’ = a
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1.d2)
d(A’D’; BC) = ?
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1.d2)
A’D’ BC; A’B BC; A’B A’D’
d(A’D’; BC) = A’B =
2a
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d(A’D; B’C) = ?
1.d3)
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1.d3)
A’D B’C; A’B’ A’D; A’B’ B’C
d(A’D; B’C) = A’B’ = a
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d(A’B’; (DCC’)) = ?
1.e)
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1.e)
A’B’ (DCC’); B’C’ A’B’; B’C’ (DCC’)
d(A’B’; (DCC’) = B’C’ = a
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d((A’AD); (B’C’C)) = ?
1.f)
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1.f)
(A’AD) (B’C’C); AB (A’AD); AB (B’C’C)
d(A’AD); (B’C’C)) = AB = a