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As shown in the figure, e, F, G and H are respectively the middle points of the edges AB, BC, CD and Da of the spatial quadrilateral ABCD. Prove that: 1. Four points e, F, G and H are coplanar 2. BD / / plane efgh 3 People's education a elective course 2-1p118 / 13
1. EH is the median line of the triangle abd,
GF is the median line of triangular CBD,
So EH and gf are parallel to BD,
So eh / / GF, namely efgh, is coplanar
2. Because EH is a straight line on the plane efgh, BD / / eh can be seen from above
So BD / / plane efgh
RELATED INFORMATIONS
- 1. 26. Known: as shown in the figure, in square ABCD, e and F are the midpoint of AB and BC respectively, and CE and DF intersect at point G 26. Known: as shown in the figure, in square ABCD, e and F are the midpoint of AB and BC respectively, and CE and DF intersect at point G Verification: ad = AG
- 2. It is known that in square ABCD, e is a point on diagonal BD, passing through e, make ef ⊥ BD, intersect BC with F, connect DF, G is the midpoint of DF, connect eg, CG
- 3. In the square ABCD, e is any point on the diagonal BD. if the circumference of the square ABCD is For m, find the perimeter of the quadrilateral EFCG
- 4. It is known that in square ABCD, e is a point on diagonal BD, passing through e, make ef ⊥ BD, intersect BC with F, connect DF, G is the midpoint of DF, connect eg, CG
- 5. In the parallelogram ABCD, e and F are the points on the edge of AD and ab respectively, and be = DF, be and DF intersect at point G
- 6. In the parallelogram ABCD, e and F are the points on the edge of AD and ab respectively, and be = DF, be and DF intersect at point G
- 7. In the parallelogram ABCD, e and F are the points on the edge of AD and ab respectively, and be = DF, be and DF intersect at point G
- 8. In the parallelogram ABCD, e and F are the points on the edge of AD and ab respectively, and be = DF, be and DF intersect at point G
- 9. The quadrilateral ABCD is a diamond. The extension of de perpendicular to ab intersects BA at point E, and DF perpendicular to BC intersects BC at point F. please guess the size of De and DF
- 10. As shown in the figure, in square ABCD, e and F are two points on BD, and be = DF
- 11. Given that the space quadrilateral ABCD E F G is the midpoint of AB BC CD ad respectively, we prove the efgh parallelogram
- 12. As shown in the figure, in ladder ABCD, ad ‖ BC and EF are the midpoint of AB and AC respectively. Connect EF and intersect AB and CD with G and h to verify: (1) eh = GF; (2) Hg = 1 / 2 (BC-AD)
- 13. If efgh is the inscribed rectangle of rectangle ABCD, and EF: FG = 3:1, AB: BC = 2:1, then ah: AE=______ ．
- 14. If efgh is the inscribed rectangle of rectangle ABCD, and EF: FG = 3:1, AB: BC = 2:1, then ah: AE=______ ．
- 15. When the quadrilateral ABCD satisfies what condition, the quadrilateral efgh is a rectangle, and EF = 2fg? And explain the reason E F G H is the midpoint of the segment AB BC CD ad respectively
- 16. If efgh is the inscribed rectangle of rectangle ABCD, and EF: FG = 3:1, AB: BC = 2:1, then ah: AE=______ ．
- 17. In cuboid, abcd-efgh, ab = 9cm, BC = 5cm, BF = 5cm BF = 4cm / find the total length of the edge perpendicular to the plane dcgh
- 18. As shown in the figure, in the cuboid abcd-efgh, ab = BC = CD = Da = 4cm, FB = 3cm, if ant a walks 6cm per second, ant B walks 5cm per second (2) If ant a starts from point a, moves along the edge in the plane ABCD, and then goes back to point a (not in motion), ant B starts from point F, moves down along the edge FB, and then moves along the edge in the plane ABCD to point a (not in motion), and two ants start at the same time, then where do they meet? (except point a) (there are three answers)
- 19. If eh = 3, EF = 4, what is the length of edge ad
- 20. As shown in the figure, fold the four corners of rectangle ABCD inward to form a seamless quadrilateral efgh, eh = 12cm, EF = 16cm, then the length of side ad is () A. 12 cm B. 16 cm C. 20 cm D. 28 cm