As shown in the figure, in the square ABCD, e is the midpoint of AD, f is on CD, and DF = 1 / 4CD BE.EF.BF To prove that be is perpendicular to ef

Let X be the side length of a square
Ed = x / 2, DF = x / 4. According to Pythagorean theorem, EF = radical 5 / 4x,
In the same way,
Be = root 5 / 2x, BF = 5 / 4x,
Then be square + EF square = be square
So the triangle bef is a right triangle
So be vertical EF
(for reference only)

RELATED INFORMATIONS

1. As shown in the figure, rotate square ABCD around point a clockwise to get square aefg, edge FG and BC intersect at point h. verification: Hg = Hb
2. As shown in the figure, rotate square ABCD around point a clockwise to get square aefg, edge FG and BC intersect at point h. verification: Hg = Hb
3. Rotate square ABCD around point a clockwise to get square aefg. Edge FG and BC intersect at point H (as shown in the figure). Is segment Hg equal to segment HB? Please observe the conjecture first, and then prove your conjecture
4. If the side length of the square is 2cm and the area of the overlapping part (quadrilateral abhg) is 3 / 4 times the root sign 3, what is the rotation angle
5. After the square ABCD rotates n degrees around point a, the square aefg, EF and CD intersect at point o.1. Connect de and Ao, and prove that De is perpendicular to AO 2. If the side length of the square is 2 and the area of the overlapping part (quadrilateral aeod) is 4 / 3 times the root sign 3, the rotation angle n is calculated Baidu knows that there is a solution to this problem, but it uses trigonometric function Here we need to use quadrilateral or Pythagorean theorem to solve
6. As shown in the figure, rotate square ABCD around point a clockwise to get square aefg, edge FG and BC intersect at point h. verification: Hg = Hb
7. Let the side length of the square ABCD be 6, and rotate 30 degrees clockwise around point a to get the square aefg, where the side FG and BC intersect at h, and find the length of BH
8. As shown in the figure, it is known that the side length of square ABCD is 10 cm, point E is on side AB, and AE = 4 cm. If point P moves from point B to point C at a speed of 2 cm / s on line BC, and point Q moves from point C to point D on line CD, let the motion time be T seconds. (1) if the motion speed of point q is equal to that of point P, after 2 seconds, are △ BPE and △ CQP identical? Please explain the reason; (2) if the velocity of point q is not equal to that of point P, then when t is the value, it can make △ BPE and △ CQP congruent; at this time, what is the velocity of point q
9. The edge CD of square ABCD connects be and DG on the edge ce of square ECGF. (1) observe the size relationship between be and DG and prove the conclusion. (2)
10. The edge CD of square ABCD connects be and DG on the edge ce of square ECGF;
11. The square ABCD and aefg common point a point Ge rotates aefg on ADAB, whether DF and BF are equal or not, it is incorrect to give a counter example Point G is on ad, point E is on AB, connect DF and BF, rotate square aefg around point a, whether DF and BF are still equal, incorrect, give a counterexample
12. If AF = 4, ab = 7, find: (1) point out the rotation center and rotation angle; (2) find the length of de; (3) what is the position relationship between be and DF? And explain the reason
13. As shown in the figure, the quadrilateral ABCD is a square, △ ADF is rotated to get △ Abe, ∠ 1 = ∠ 2, please judge: (1) the shape of △ AEG; (2) the relationship between Ag and BG + DF
14. As shown in the figure, ABCD is a square with side length of 2a, Pb ⊥ plane ABCD, Ma ∥ Pb, and Pb = 2mA = 2A, e is the midpoint of PD Verification: me ‖ plane ABCD Solution: cosine value of dihedral angle formed by plane PMD and plane ABCD Can you write me the specific process of the first question? I really don't understand. Please
15. In the geometry shown in the figure, the quadrilateral ABCD is a square, Ma ⊥ plane ABCD, PD ∥ Ma, e, G, f are the midpoint of MB, Pb, PC respectively, and ad = PD = 2mA. (I) verification: plane EFG ⊥ plane PDC; (II) calculation of the volume ratio of triangular pyramid p-mab and quadrangular pyramid p-abcd
16. As shown in the figure, the quadrilateral ABCD, cdef and efgh are all square. (1) is △ ACF similar to △ GCA? Talk about your reasons; (2) find the degree of ∠ 1 + 2
17. As shown in the figure, the quadrilateral ABCD, cdef and efgh are all square. (1) is △ ACF similar to △ GCA? Talk about your reasons; (2) find the degree of ∠ 1 + 2
18. Quadrilateral ABCD, cdef, efgh are square, connect AC, AF, Ag, calculate the degree of angle AFB + angle AGB, thank you
19. As shown in the figure, the quadrilateral ABCD, cdef and efgh are all square. (1) is △ ACF similar to △ GCA? Talk about your reasons; (2) find the degree of ∠ 1 + 2
20. As shown in the figure, the quadrilateral ABCD, cdef and efgh are all square. (1) is △ ACF similar to △ GCA? Talk about your reasons; (2) find the degree of ∠ 1 + 2