As shown in the figure, it is known that the quadrilateral ABCD is a diamond, f is the intersection of a point DF on AB, AC is on e, and it is proved that ∠ AFD = ∠ CBF

It is proved that: ∵ - CBE is the outer angle of △ BFE (known) ∵ - CBE = ∵ - bef + ∵ - BFE (an outer angle of triangle is equal to the sum of two non adjacent inner angles). ∵ - AFD = ∵ - BFE (known) ∵ - AFD = ∵ CBE (equivalent substitution) it is proved that connecting BD, because the quadrilateral ABCD is a diamond, AC vertically bisects BD, BD bisects ∵ ABC, x0d so be = De, so ∵ - EBD = ∵ EDB, ∵ CBD =

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1. As shown in the figure, known quadrilateral ABCD is diamond, de ⊥ AB, DF ⊥ BC, please explain the quantitative relationship between be and BF
2. As shown in the figure, in the plane rectangular coordinate system, the area of rectangular ABCO is 15, the side OA is larger than OC by 2. E is the midpoint of BC, the ⊙ o 'intersection X axis with OE as the diameter is at point D, and DF ⊥ AE is at point F through point D. (1) calculate the length of OA and OC; (2) prove that DF is the tangent of ⊙ o'
3. As shown in the figure, in the plane rectangular coordinate system, the line y = 23x - 23 intersects with the edges OC and BC of the rectangular ABCO at points E and f respectively. If OA = 3 and OC = 4 are known, then the area of △ CEF is () A、6 B、3 C、12 D、 43
4. In the plane rectangular coordinate system, the area of △ CEF when the line y = 2 / 3x-2 / 3 intersects with the edge OC and BC of rectangular ABCO and points E and F are known as OA = 3 and OC = 4 respectively
5. As shown in the figure, oabc is a rectangular piece of paper, where OA = 8 and OC = 4. Through folding, point C coincides with point a, and the crease is ef (1). Find out the length of OE (2) And prove (3) whether there is a moving point P in the straight line where EF is located, so that the value of | pb-pc | is the maximum. If not, please explain the reason; if so, calculate the coordinates of point P
6. In the rectangular coordinate system, there is a rectangle oabc, OA = 2, OC = 1, and the coordinate of point P is (0, - 1) (1) Finding the function analytic expression of the straight line PB (2) If the line L passing through P intersects with BC, and the ratio of the area of the rectangular oabc divided into parts is 1:4, the analytic function of the line L is obtained
7. There are seven planes with the same distance from the four vertices of the space quadrilateral ABCD
8. ABCD is a square with side length of 4, e and F are the midpoint of AB and ad, GC is vertical to plane ABCD, GC is equal to 2, find the distance from B to plane EFG?
9. Let e be the midpoint of AD, a right: b right = 2:3, and find the value of Ag: GC
10. Let e be the midpoint of AD, a right: b right = 2:3, and find the value of Ag: GC
11. It is known that, as shown in the figure, the quadrilateral ABCD is a diamond, f is a point on AB, DF intersects AC with E
12. As shown in the figure, two pieces of paper of equal width are crossed and overlapped. The overlapped part is a quadrilateral. Is ABCD a diamond? Is it a proof, not a reason
13. As shown in the figure, is the quadrilateral ABCD obtained by superposition of two rectangles of equal width a diamond? Prove your conclusion An engineering team is planning to repair BM every day. Due to weather, cm (C
14. As shown in the figure, two pieces of paper of equal width are crossed and overlapped, and the quadrilateral ABCD of the overlapped part is______ Shape
15. As shown in the picture, two pieces of paper of equal width are crossed and overlapped. Is the overlapped part ABCD a diamond? Please prove it
16. The side length of the square ABCD is a. place a vertex of the square omnp large enough on the symmetric center O of the square ABCD The side length of square ABCD is a Operation and calculation: place a vertex of the square omnp large enough on the symmetric center O of the square ABCD, and OM ⊥ BC, Op ⊥ DC. Try to find the area of the quadrilateral OECF of the overlapping part of two squares Thinking and exploration: if the square omnp is rotated at any angle around point O, is be equal to CF? Why? Can we find the area of quadrilateral OECF? What do you find?
17. The vertex B and C of square ABCD are on the positive half axis of X axis, and a and D are on the parabola y = - 2 / 3x & # 178; + 8 / 3x
18. In the plane rectangular coordinate system, the coordinates of vertex B and D in square ABCD are (0,0), (2,0) respectively, and a and C are symmetric about X axis Finding the coordinates of two points a and C (using different methods)
19. Known: as shown in the figure, in the plane rectangular coordinate system xoy, the side length of square ABCD is 4, its vertex a moves on the positive half axis of X axis, and vertex D moves on the Y axis (points a and d do not coincide with the origin), B and C are in the first quadrant, diagonal AC and BD intersect at point P, connecting Op Q: when OA
20. Calculation: 27 degrees, 42 minutes, 30 seconds + 1070 minutes; 63 degrees, 36 minutes - 36.36 degrees, hurry, if correct, add 50, hurry