As shown in the figure, the diagonal lines AC and BD of rectangular ABCD intersect at point O, EF ⊥ BD at point O, ad at point E, BC at point F, and EF = BF

In △ AOE and △ COF, in △ AOE and △ COF, in △ AOE and △ COF, in △ AOE and △ COF, in △ AOE and △ COF, in △ AOE and △ COF, OAE = ocfoa = ocfoa = OC ∈ AOE = OC ∈ AOE 8780 \8780 \8780 \\\\\\\\\\ \\\\\\\\\\\\\\\\\\bfo - ∠ OCB = 60 ° - 30 ° = 30 ° ，∴∠OCB=∠COF，∴OF=CF．

RELATED INFORMATIONS

1. As shown in the figure, in square ABCD, the diagonal lines AC and BD intersect at point O, and the points EF are on AC and BD respectively, and BF = CE connects be, AF.AF There is a relation between be and quantity
2. 1. As shown in the figure, the quadrilateral ABCD is a rectangle, ∠ EDC = ∠ cab, ∠ Dec = 90 ° (1) prove: AC ‖ de; (2) make BF ⊥ AC at point F through point B, connect
3. ABCD is a rectangle ∠ EDC = ∠ cab ∠ Dec = 90 ° (1) verification: AC ‖ de (2) through B as BF ⊥ AC connected to f to judge the shape of becf and explain the reason
4. The quadrilateral ABCD is a rectangle,
5. As shown in the figure, the quadrilateral ABCD is a rectangle, ∠ EDC = ∠ cab, ∠ Dec = 90 ° (1) verification: AC ‖ de（ 2) Make BF ⊥ AC at point F through point B, connect EF, try to judge the shape of quadrilateral BCEF, please explain the reason (do not judge parallelogram)
6. As shown in the figure, the quadrilateral ABCD is a rectangle, ∠ EDC = ∠ cab, ∠ Dec = 90 ° (1) Verification: AC ‖ de; (2) Make BF ⊥ AC at point F through point B, connect EF, try to judge the shape of quadrilateral BCEF, and explain the reason
7. As shown in the figure, in rectangle ABCD, AE = BF = 3, EF ⊥ ed intersects BC at point F, and the circumference of rectangle is 22. Calculate the length of EF
8. It is known that the circumference of rectangle ABCD is 18, e and F are the points on the edges AB and BC respectively, and AE = BF = 1. If EF is perpendicular to BD, the area of this rectangle can be calculated
9. As shown in the figure, ▱ ABCD, if EF crosses the intersection of diagonal lines o, ab = 4, ad = 3, of = 1.3, then the perimeter of quadrilateral BCEF is______ ．
10. In the parallelogram ABCD, if EF passes through the intersection of diagonals o, ab = 4, ad = 3, the perimeter of quadrilateral BCEF = 9.6, the length of of of can be obtained
11. Parallelogram ABCD parallelogram abef is on the same side AB, m, n are on the diagonal AC, BF respectively, and am: AC = FN: FB to prove Mn / / plane ADF
12. ABCD and abef are parallelograms, m and N are the points on diagonal AC and BF respectively, and am: FN = AC: BF
13. As shown in the figure, let ABCD and abef be parallelograms, they are not in the same plane, m and N are the points on the diagonal AC and BF respectively, and am: FN = AC: BF (Continued), prove: Mn ‖ plane bec
14. It is known that ABCD and abef are two squares and not in the same plane, m and N are the points on the diagonal AC and FB respectively, and am = FN It is suggested that the extension line connecting an and be should be connected to g
15. As shown in the figure, the planes of two congruent squares ABCD and abef intersect AB, m ∈ AC, n ∈ FB, and am = FN
16. In the parallelogram ABCD, EF is the midpoint of AD and BC respectively The intersection of the center line BD and CE of triangle ABC with O, F and G is the midpoint of OB and OC respectively
17. In parallelogram ABCD, de ⊥ AC in E, BF ⊥ AC in F, connect be ` DF, then be ∥ DF? Be = DF? Try to explain your reason
18. In a parallelogram, points E and F are on AB and CD respectively, DF = be. Is the quadrilateral debf a parallelogram? Tell me your reason
19. As shown in the figure, in the angle ABCD, the points E and F are on AB and CD respectively, be = DF. It is proved that the quadrilateral debf is a parallelogram The graph is inside, and the line DB is removed
20. The quadrilateral ABCD is a parallelogram, de ⊥ AC, BF ⊥ AC, and the perpendicular feet are e, F, be and DF respectively