The quadrilateral ABCD ABCD and BEFC are both squares, and the point P is the moving point on the side of AB (not coincident with the points A and B). When the vertical line of DP passing through the point P intersects the diagonal BF at the point Q (1), as shown in Figure ①, when the point P is the midpoint of AB: ① DP=PQ can be known through measurement, please prove that ② if m is the midpoint of AD, MP = can be known. When the point P is at any position on the AB side, other conditions remain unchanged. Is the quantitative relationship between two line segments in (1) valid? If yes, please prove it; If it is not true, try to explain the reason 2: AB=c,BC=a,CA=b,AD⊥BC in △abc, and prove c2=a2+b2-2abcosc 3: As shown in the figure, BD is the bisector of ∠ABC, DE⊥AB is at point E, and DF ⊥.4 Verification: DB=2CE 5: In triangle ABC, AB=3, AC=4, BC=5, triangle, triangle ABD, triangle ACE, triangle BCF. Si= 1, the number of adoptees. Is to find the area, not to prove the parallelogram 6: in the acute triangle ABC, if ∠ a >; ∠B& gt； ∠C, verification: ∠ a > 60，∠B& gt； ∠ C7: Prove that the distance from a vertex of a triangle to the vertical center is equal to twice the distance from the outer center to the opposite side of this vertex. The general idea is as follows: in △ ADE, ∠DAE=Rt, AC is high, B is on the extension line of DE, ∠ BAE = ∠ D, and it is proved that: Be 2/EC 2 = BD/DC9:.1cubic +2 cubic ... +N cubic = 6 10: It is proved that the difference between any two sides of a triangle is smaller than the third side 1 1: In quadrilateral ABCD, the two diagonals are equal, and the acute angle between them is 60 degrees. Excuse me, what is the relationship between the sum of the lengths of two sides facing a 60-degree angle and one of the diagonals? Please prove your conclusion in detail! ! 12: point p is the intersection of bisectors of angles ∠ABC and ∠ACB. It is proved that ∠ P = 90+2 ∠ A 13: As shown in the figure, triangles ABC, DBF and EFC are equilateral triangles. Please prove it. Let f (a 1) = f (A2) = f (A3) =1,and let b be any integer not equal to a1,a2, a3. Try to prove that f(b) is not = 1? 15: arbitrary triangle abc, where three bisectors of internal angles AD, BE and CF intersect at point h, and point h is taken as the vertical line of ac, and the vertical foot is g, which proves whether the angles of ahe and chg are equal. Why 16: The triangle is inscribed with a circle O, AE is the diameter of the circle O, and AD is the height of the BC side in the triangle. It is proved that AC times BE=AE. 17: Known: in triangle ABC, AC = BC, angle ACB = 90 degrees, D is the midpoint of AC, point F is on AB, and angle FDA= = angle BDC .. Prove: CF is perpendicular to BD. 18: Known proposition: If quadratic function y=ax2 (where 2 represents square), Then y = a (x-x 1) (x-x2) judges whether this proposition holds, and explains the reason 19: It is known that A and B are real numbers, and AB=0 is satisfied, which proves that at least one of A and B is 0. 20: any triangle ABC D is the midpoint of the BC side, and the bisector connecting AD ∠ADB, AB and E ∠ the bisector of ∠ADC, AC and F proves: Be+FC > EF.