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

Hehe, I have done this... Condition: AC ⊥ BD, and AC = 2bd ∵ e, F, G, h are the midpoint of line AB, BC, CD, ad, respectively, connecting EF, eh, FG, GH. ∥ EF, eh, FG, GH are the median lines of △ abd, △ ABC, △ BCD, △ ADC ∥ eh ∥ BD, FG ∥ BD, EF ∥ AC, GH ∥ AC, that is eh ∥ FG, e

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1. If efgh is the inscribed rectangle of rectangle ABCD, and EF: FG = 3:1, AB: BC = 2:1, then ah: AE=______ ．
2. If efgh is the inscribed rectangle of rectangle ABCD, and EF: FG = 3:1, AB: BC = 2:1, then ah: AE=______ ．
3. 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)
4. Given that the space quadrilateral ABCD E F G is the midpoint of AB BC CD ad respectively, we prove the efgh parallelogram
5. 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
6. 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
7. 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
8. 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
9. 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
10. 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
11. If efgh is the inscribed rectangle of rectangle ABCD, and EF: FG = 3:1, AB: BC = 2:1, then ah: AE=______ ．
12. In cuboid, abcd-efgh, ab = 9cm, BC = 5cm, BF = 5cm BF = 4cm / find the total length of the edge perpendicular to the plane dcgh
13. 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)
14. If eh = 3, EF = 4, what is the length of edge ad
15. 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
16. As shown in the figure, the four corners of rectangle ABCD are folded inward to form a seamless and overlapping quadrilateral efgh. If eh = 3cm and EF = 4cm, the length of side AB is () A. 4.6cmb. 4.8cmc. 5.0cmd
17. In the trapezoidal ABCD, if ad ‖ BC, diagonal AC ⊥ BD, and AC = 6cm, BD = 8cm, the length of the trapezoidal median line is equal to
18. In the trapezoid ABCD, AB is parallel to BC, the diagonal AC is perpendicular to BD, and AC is equal to 8 cm, BD is equal to 6 cm. What is the height of this trapezoid?
19. In trapezoidal ABCD, CD is equal to AB, if angle a = 45 degrees, angle B = 60 degrees, BC = 5, find the length of AD and ab
20. P is any point on the side BC of the square ABCD, and PE is perpendicular to BD intersecting BDE, PF is perpendicular to AC intersecting AC, if AC = 10, EP = FP