The triangle ABCD is a square, PD ⊥ face ABCD, PD = PC, e is the midpoint of PC,
Prove: because PD ⊥ plane ABCD, so PD ⊥ BC; because quadrilateral ABCD is square, so BC ⊥ DC; from PD ⊥ BC, BC ⊥ DC, we can know BC ⊥ plane PDC, because De is on plane PDC, so BC ⊥ de. because PD = DC, so triangle PDC is isosceles triangle, and because e is the midpoint of PC, so de ⊥ PC
RELATED INFORMATIONS
- 1. 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
- 2. The diamond ABCD is on the plane a, PA is perpendicular to a, and PC is perpendicular to BD
- 3. 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
- 4. 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
- 5. In rectangle ABCD, take any point P, connect AP, BP, CP, DP, ask the relationship of AP, BP, CP, DP
- 6. In rectangular ABCD, there is a point P, AP = 3, DP = 4, CP = 5, BP =? How to calculate?
- 7. There is a point in rectangle ABCD, P AP = 8 bp = 7 CP = 6 DP =?
- 8. 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
- 9. 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)
- 10. 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
- 11. The edge length of cube abcd-a'b'c'd 'is 1. Find the distance from point C to plane c'bd
- 12. 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
- 13. 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!
- 14. How many planes are equal to the four vertices of the space quadrilateral ABCD?
- 15. 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
- 16. 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
- 17. 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
- 18. 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?
- 19. 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?
- 20. Through the vertex a of square ABCD, do PA ⊥ plane ABCD, PA = AB = 1, find the dihedral angle formed by plane APB and plane cpd