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Given that PA ⊥ square ABCD, if AB = PA, then the dihedral angle of plane PAB and plane PCD is
Do you know the area projective theorem? Since the projective of D on the plane PAB is a and the projective of C is B, it should be easy for you to know that the triangle PCD is a right triangle. Find out that its area is the square of two AB under two-thirds root sign, and the area of PAB is the square of two-thirds ab. then cosa = two-thirds root. A = 45 degrees
You can also see that planar pad, PCD and PAB are vertical, which is easy to know
RELATED INFORMATIONS
- 1. If the line AP is perpendicular to the plane ABCD through the vertex a of the square ABCD, and AP = AB, then what is the dihedral angle between the plane ABP and the plane CDP? (Figure)
- 2. If the vertex a of the square ABCD passes through the AP vertical plane ABCD and AP = AB, then the degree of the dihedral angle between the plane ABP and the plane DCP is Draw a picture
- 3. If the vertex a of the square ABCD passes through the line AP ⊥ plane ABCD, and AP = AB, then the degree of the dihedral angle formed by the plane ABP and the plane CDP is If you do well, you can pay me a picture, because I don't know how to draw a plane CDP
- 4. 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
- 5. 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?
- 6. 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?
- 7. 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
- 8. 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
- 9. 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
- 10. How many planes are equal to the four vertices of the space quadrilateral ABCD?
- 11. Through the vertex a of the square ABCD, make the line PA ⊥ plane ABC, and PA = Pb, then the degree of the sharp dihedral angle formed by plane ABC and plane PCD is? Sorry, wrong number. It's not pa = Pb, it's PA = ab
- 12. PA is perpendicular to the plane of the square ABCD with side length a, PA = a, then the size of the dihedral angle b-pc-d is It needs a rough process
- 13. If the bottom of p-abcd is a parallelogram, the bottom of PA ⊥ is ABCD, the point E is on the side edge PC, and PE = 13pc, then VP − bdevp − ABCD=______ ．
- 14. The bottom of p-abcd is a parallelogram, the bottom of PA ⊥ is ABCD, e is a point on PA, and the section of PC ∥ is BDE Find the volume ratio of the two parts of the pyramid p-abcd divided by the section BDE
- 15. The bottom surface of the pyramid p-abcd is a square with side length 1, and the side edge PA is perpendicular to the bottom surface ABCD. Moreover, PA = 2. If e is the midpoint of PA, we prove the plane BDE
- 16. P is a point outside the parallelogram ABCD, and Q is the midpoint of PA
- 17. P is a point out of the plane of the parallelogram ABCD. Find a point E on PC to make the PA ‖ face be, and give the proof
- 18. P is the point out of the plane of the parallelogram ABCD, and Q is the midpoint of PA
- 19. P is a point outside the parallelogram ABCD, and Q is the midpoint of PA
- 20. Let p be a point in the square ABCD, and the distances from point P to vertex ABC are 1, 2 and 3 respectively