Given that the side length of square ABCD is 2 and point P is a point on diagonal AC, the maximum value of (. AP +. BD) ·(. Pb +. PD) is______

Take a as the coordinate origin, AB as the positive direction of X axis, ad as the positive direction of Y axis to establish a rectangular coordinate system, then a (0,0), B (2,0), C (2,2), D (0,2), ∵ P points have diagonal AC, let P (x, x), 0 < x < 2, so. AP = (x, x),. BD = (- 2,2),. Pb = (2-x, - x),. P

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1. If the side length of square ABCD is 1 and point P moves on line AC, then the value range of AP & nbsp; · & nbsp; (Pb + PD) is______ ．
2. In known trapezoidal ABCD, ad is parallel to BC, angle ABC = 60 degrees, ab = AD + BC = 4, M is the midpoint, find the size of 1 angle dam, the length of AM and BM
3. As shown in the following figure: in trapezoidal ABCD, the area of triangle AEC is 4, the area of triangle CED is 6, and the area of triangle bed is 9? In the picture, the two diagonals are pulled up and divided into four triangles. There are two diagonals A and C (from left to right) at the top and two diagonals B and D at the bottom. The intersection of the diagonals is e
4. P is a point inside the square ABCD and a point e outside the square ABCD. Find the degree of angle BPE P is a point inside the square ABCD, and there is a point e outside the square ABCD, satisfying the angle Abe = angle CBP, be = BP, and finding the degree of angle BPE
5. As shown in the figure, e is an edge point in the square ABCD. If the triangle Abe is an equilateral triangle, find the degree of the angle BCE
6. 1. As shown in the figure, e is a point in the square ABCD, and △ Abe is an equilateral triangle. Think about the relationship between ∠ DCE and ∠ CEB, and explain the reason. 2 1. As shown in the figure, e is a point in the square ABCD, and △ Abe is an equilateral triangle. Think about the relationship between ∠ DCE and ∠ CEB, and explain the reason 2. As shown in the figure, the upper bottom ad of the isosceles trapezoid ABCD = 1, the lower bottom BC = 3, the diagonal AC ⊥ BD, find the height and length of the isosceles trapezoid
7. E is a point in the square ABCD, and the triangle Abe is an equilateral triangle, connecting CE and De, then ∠ CBE=____ ,∠DCE=____ ,∠CED=____
8. In the square ABCD, there is a point E, △ EAB is an equilateral triangle, ∠ CED = several degrees
9. As shown in the figure, given a point E in the square ABCD, and AE = EB = AB, find the degree of ∠ EDC and ∠ ECB
10. As shown in the figure, the angle EDC is determined by making an equilateral triangle Abe in square ABCD connecting de and CE=
11. If the parallelogram ABCD and EF cross the focus o, ab = 3, BC = 5 and OE = 2 of the diagonal, what is the perimeter of the parallelogram ADFE
12. If AB = 5, BC = 7, OE = 2, then the perimeter of EFDC is () A.14 B.15 C.16 D.18
13. 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
14. 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______ ．
15. 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
16. 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
17. 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
18. 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)
19. The quadrilateral ABCD is a rectangle,
20. 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