As shown in the figure, fold the △ ABC paper along de. when point a falls inside the quadrilateral bced, try to explore,

Let G be the point where a falls inside
In △ ABC, ∠ B + ∠ C = 180 - ∠ a
In △ GDE, ∠ GDE + ∠ GED = 180 - g = 180 - A
In the quadrilateral bced, 1 + 2 = 360 - B - C - GDE - GED = 2 - A

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1. (1) As shown in the figure, the triangle ABC paper is folded along De to form figure 1. At this time, point a falls inside the quadrilateral bced, and there is a quantitative relationship between angle A and angle 1 and angle 2, which remains unchanged. Find out the quantitative relationship and explain the reason; (2) If the point a falls on be or CD, write the relationship between angle A and angle 2, angle A and angle 1, and explain the reason; (3) If folded into Figure 4, write the relationship between angle A and angle 1, angle 2, and explain the reason; (3) if folded into figure 5, write the relationship between angle A and angle 1, angle 2, and explain the reason
2. As shown in the figure, fold a triangular piece of paper ABC along De, and point a falls inside the quadrilateral bced (1). If ∠ a = α, find ∠ 1 + 2
3. It is known that, as shown in the figure, in triangle ABC de / / BC, and the area of triangle ABC is equal to the area of trapezoid bced, the ratio of De to BC is calculated
4. As shown in the figure, in RT △ ABC, the area sum of square Adec and square bcfg is () A. 150cm2b. 200cm2c. 225cm2d. Unable to calculate
5. As shown in the figure, make a square from the three sides of RT △ ABC. If the side length of the largest square is 8cm, then the sum of the areas of square m and square n is______ cm2．
6. It is known that a [0, a], [b, 0], [C, 0] are the three vertices of △ ABC. A straight line L passing through the origin o of the coordinate intersects with the line AB at point D, and is the extension of ca (1) if the angle BOD is 45 °, calculate the degree of BPD
7. As shown in Figure 6, in the plane rectangular coordinate system, the three vertices of △ ABC are a (m, 4) B (6,0) C (- m, - 4), and AC passes through the origin o, BH is perpendicular to AC and H Find the value of AC * BH () to get the positive solution and offer a reward of 40
8. It is known that G is the center of gravity of the triangle ABC and O is any point in the plane
9. The plane passes through the center of gravity of the triangle ABC, B and C are on the same side of the plane, and a is on the other side of the plane, If the distances from a, B and C to the plane are a, B and C respectively, then the relationship between a, B and C is
10. As shown in the figure, ad is the angular bisector of ∠ cab, de ‖ AB, DF ‖ AC, EF intersects ad at point O. excuse me: (1) is do the angular bisector of ∠ EDF? If so, please prove it; if not, please explain the reason. (2) if the conclusion is exchanged with any of the conditions in which ad is the angular bisector of cab, de ‖ AB, DF ‖ AC, is the proposition correct?
11. As shown in the figure, in △ ABC, ∠ C = 90 °, D is the point on AC, de ⊥ AB is at point E. if AB = 10, BC = 6, de = 2, calculate the area of quadrilateral DEBC
12. As shown in the figure, in △ ABC, ∠ C = 90 ° de bisects AB vertically, intersects BC with E, ab = 20, AC = 12. (1) find the length of be; (2) find the area of quadrilateral Adec
13. It is known that in ABC triangle, D and E are AC = 7, ∠ ABC = 120 °, AE = BC and Sina = 3 √ 3 / 14 on AC and ab respectively, and the area of quadrilateral DEBC is calculated Please, the sooner the better,
14. In triangle ABC, D and E are the midpoint of AB and AC respectively, then the area ratio of triangle ade to quadrilateral DEBC is ()
15. The circumference of circle O is equal to 4 π cm. Find the side length, side center distance and area of its inscribed regular triangle ABC
16. The perimeter sum of an equilateral triangle ABC and a square defg is 95 decimeters. AB: de = 1:4. What is the side length of an equilateral triangle
17. As shown in the figure, the triangle ABC is a right triangle, the quadrilateral EDFC is a square, the sum of the areas of the two shadow triangles is 32 square centimeters, ad: DB = 4:1, find the length of AD
18. Triangle ABC is a right triangle, quadrilateral ACDE, fgba are square, ab = 8 cm, BC = 6 cm, triangle AEF
19. As shown in the figure, the triangle ABC is a right triangle, and the quadrilateral befd is a square. Given that the lengths of AB and BC are 12 cm and 20 cm respectively, what is the square area?
20. As shown in the figure, in the right triangle ABC, e is the intersection of the bisectors of two acute angles, ed ⊥ BC is D, EF ⊥ AC is F. can you explain that the quadrilateral cdef is a square?