![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
As shown in the figure, the quadrilateral ABCD is a square, PD ⊥ plane ABCD, EC ∥ PD, and PD = 2ec. (I) prove: plane PBE ⊥ plane PBD; (II) if the dihedral angle p-ab-d is 45 °, find the sine value of the angle between the straight line PA and the plane PBE
(1) Connect AC to BD at point F, take the midpoint n of Pb, connect en, FN. ∵ FBD as the midpoint, ∥ NF ∥ PD, NF = 12pd, EC = 12pd ∥ quadrilateral nfce as parallelogram ∥ ne ∥ FC ∥ DB ⊥ AC, PD ⊥ face ABCD, AC ⊂ face ABCD, ≁ AC ⊥ PD, PD ∩ BD = D, ≁ AC ⊥ PBD, namely FC
RELATED INFORMATIONS
- 1. The diamond ABCD is on the plane a, PA is perpendicular to a, and PC is perpendicular to BD
- 2. In the pyramid p-abcd, the bottom surface ABCD is a distance shape, PA ⊥ ABCD, the point E is on PC, and the PC ⊥ surface BDE In the pyramid p-abcd, the bottom surface ABCD is a distance shape, PA ⊥ ABCD, the point E is on PC, and the PC ⊥ surface BDE is: ① prove: the BD ⊥ surface PAC; ② if PA = 1, ad = 2, find: the tangent value of the face angle b-pc-a
- 3. Point P is a point in the square ABCD, connecting AP, BP, CP, DP. If △ ABP is an equilateral triangle, find the degree of ∠ cpd
- 4. In rectangle ABCD, take any point P, connect AP, BP, CP, DP, ask the relationship of AP, BP, CP, DP
- 5. In rectangular ABCD, there is a point P, AP = 3, DP = 4, CP = 5, BP =? How to calculate?
- 6. There is a point in rectangle ABCD, P AP = 8 bp = 7 CP = 6 DP =?
- 7. There is a square ABCD whose side length is Q. P is a point on the diagonal BD. when p is at what position, the value of AP + BP + CP is the minimum
- 8. It is known that square ABCD is inscribed at O, and point P is a point on inferior arc ad. it connects AP, BP, CP and (AP + CP) / BP (important process)
- 9. P is a moving point outside the rectangular ABCD, and satisfies the AP vertical CP BP.DP When point P changes, does the degree of angle BPD change? If not, calculate the degree of angle BPD; if not, calculate the range of change
- 10. As shown in the figure, in square ABCD, points E and F are on edge BC and CD respectively. If AE = 4, EF = 3 and AF = 5, then the area of square ABCD is equal to () A. 22516B. 25615C. 25617D. 28916
- 11. The triangle ABCD is a square, PD ⊥ face ABCD, PD = PC, e is the midpoint of PC,
- 12. The edge length of cube abcd-a'b'c'd 'is 1. Find the distance from point C to plane c'bd
- 13. In the cube abcd-a1b1c1d1 with edge length 1, (1) find the distance from point a to plane BD1; (2) find the distance from point A1 to plane ab1d1; (3) find the distance between plane ab1d1 and plane BC1D; (4) find the distance from line AB to cda1b1
- 14. Find a point O in the quadrilateral ABCD to minimize the sum of the distances between it and the four vertices of the quadrilateral, and please give your reasons It's best to draw a picture to illustrate!
- 15. How many planes are equal to the four vertices of the space quadrilateral ABCD?
- 16. Given that PA is perpendicular to the plane of rectangle ABCD, AB is equal to four, BC is equal to three, PA is equal to one, the distance from P to straight line BD is
- 17. PA is perpendicular to the plane of rectangle ABCD, and ab = 3cm, ad = 4cm, PA = 6 / 5 root 21cm. Calculate the distance from point P to BC and BD respectively
- 18. Given that PA is perpendicular to the plane of rectangle ABCD, and ab = a, ad = B, PA = 2c, find the distance from the midpoint Q of PA to the straight line BD
- 19. Given that ABCD is a rectangle, ab = a, ad = B, PA ⊥ plane ABC, PA = C, then the distance from P to BC is? And the distance from P to BD is?
- 20. Given that ABCD is a rectangle, ab = a, ad = B, PA ⊥ plane ABC, PA = C, then the distance from point P to BC and BD is How to find two distances?