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As shown in the figure, in the four prism abcd-a1b1c1d1, d1d ⊥ bottom surface ABCD, bottom surface ABCD is square, and ab = 1, d1d = 2. (1) find the angle between the line D1b and the plane ABCD; (2) prove: AC ⊥ plane bb1d
(1) ∵ d1d ⊥ plane ABCD, BD is the projection of D1b on the bottom surface ABCD, and ∵ d1bd is the angle formed by the straight line D1b and plane ABCD. In the right triangle d1bd, if BD = 2 and d1d = 2, then Tan ∵ d1bd = d1dbd = 1 and ∵ d1bd = 45 degrees, that is, the angle formed by the straight line D1b and plane ABCD is 45 degrees
In the cube abcd-a1, B1, C1 and D1, let m and n be the midpoint of edge A1B1 and c1d1 respectively, and E and f be edge B respectively
(1) E, F, B, D, four points coplanar (2) plane amn parallel plane efdb
1: Draw a cube by yourself, mark a B C D (clockwise) at the bottom corner on the left side of the upper bottom, A1 B1 C1 D1 on the lower bottom, and then mark m n e f (N and f coincide). Connect b1d1, because EF is the midpoint respectively, EF is the median line of triangle c1b1d1, so EF is parallel to b1d1 and
10. As shown in the figure, the side length of square ABCD is 3cm. Make the trisection points A1, B1, C1, D1 on the sides AB, BC, CD, Da to get square a1b1c1d1, and then take the trisection points A2, B2, C2, D2 on the sides A1B1, b1c1, c1d1, d1a1 to get square a2b2c2d2. If this continues, get square a3b3c3d3 (1) Find the length of the edge A1B1, a2b2, a3b3; (2) find the length of the square anbncndn
(1) A1B1 = root sign (square of ab - 4 * (1 / 2 * 3 / AB * 3 / 2Ab)) a
=(radical 5) a
A2b2 = root sign (square of A1B1 - 4 * (1 / 2 * 3 / 3 A1B1 * 2 / 3 A1B1)) a
=5 / 3 A
A3b3 = root sign (square of a2b2 - 4 * (1 / 2 * 3 / 2 a2b2 * 2 / 3 a2b2)) a
=(5 / 9 root 5) a
(2) A1B1 = 3 * 3 root 5 * 3 root 5 = root 5A
A2b2 = 3 * 3 root 5 * 3 root 5 = 3 / 5A
A3b3 = 3 * 3 root 5 * 3 root 5 * 3 root 5 * 3 root 5 = (9 / 5 root 5) a
Let anbn = n times a of 3 * (3 / 3 root sign 5)
Anbn / an-1bn-1 = 3 * (3 / 3 root 5) of n-th A / 3 * (3 / 3 root 5) of n-th a = 3 / 3 root 5
So the nth a of anbn = 3 * (3 / 3 root sign 5) is correct
RELATED INFORMATIONS
- 1. In the quadrilateral ABCD, AC ⊥ BD, points A1, B1, C1 and D1 are the midpoint of AB, BC, CD and Da respectively. If AC = 18 and BD = 20, then In the quadrilateral ABCD, AC ⊥ BD, points A1, B1, C1 and D1 are the midpoint of AB, BC, CD and Da respectively. If AC = 18 and BD = 20, the area of quadrilateral a1b1c1d1 is ()
- 2. In the cube abcd-a1b1c1d1, e and F are the midpoint of edge BC and c1d1 respectively （2）AC⊥EF (3) Plane aa1c1c ⊥ plane ab1d1
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- 11. As shown in the figure, the square prism abcd-a1b1c1d1 is known, the point E is the midpoint of edge d1d, A1A = radical 2a, ab = A. (1) verification: D1
- 12. In the cube abcd-a1b1c1d1, e is the midpoint of d1d, f is the midpoint of AB, and EC is at an angle with FB1
- 13. In cube ABCD_ In a1b1c1d1, if the edge length is a, P is the midpoint of edge Aa1, and Q is any point on edge BB1, then the minimum value of PQ + QC is?
- 14. Make a plane intersection aa1d1d through the edge BB1 of square abcd-a1b1c1d1, and verify: EF / / BB1
- 15. As shown in the figure, in the cube ABCD – a1b1c1d1, verify that plane aca1c1 is perpendicular to plane a1bd
- 16. In the cube abcd-a1b1c1d1, M is the midpoint of Aa1 ditto
- 17. In the cube abcd-a1b1c1d1, M is the midpoint of Aa1
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- 20. It is known that in the cube abcd-a1b1c1d1, the edge length is 1 and the area of triangle a1bc is calculated