14 As shown in the figure, the quadrilateral ABCD is an isosceles trapezoid, ad∨BC, AB=CD, diagonal AC and BD intersect at point O, AC⊥BD, DH ⊥ BC. (1) Verification: DH = (AD+BC) (1) If AC=6, find the area of trapezoidal ABCD. 15. When discussing the problem of rectangular origami, a research and study group rotates the vertex of a right triangle around the intersection o of the diagonal of a rectangular ABCD (AB < BC) (①→→→→→→→→ ③), where m and n are the intersections of the right side of the right triangle and the sides CD and BC of the rectangular ABCD, respectively. (1) The members of the research team unexpectedly found that in Figure ① (the right angle of the triangle coincides with OD), BN 2 =CD 2 +CN 2, and in Figure ③ (one side of the triangle coincides with OC), CN 2 =BN 2 +CD 2. Please explain a conclusion that this member found in Figures ① and ③. Figure ① Figure ② Figure ③ (2) Try to explore the quantitative relationship between the four line segments BN, CN, CM and DM in Figure ②, write your conclusion and explain the reasons. (3) Change the rectangular ABCD into a square ABCD with the side length of 1, rotate the right-angled vertex of the right-angled triangle around the O point to Figure ④, and the two right-angled sides intersect AB and BC at M and N respectively, and directly write out the quantitative relationship between the four line segments BN, CN, CM and DM (without proof). Figure ④ 16, at □ABCD and □ BC. (1) As shown in Figure ①, when α = 900, the quantitative relationship between ME and MC is ∠DME and ∠AEM. (2) As shown in Figure ②, when 600 < α < 900, may I ask: ① What is the quantitative relationship between ME and MC at this time? ② What is the quantitative relationship between ②∠DME, ∠AEM and α? Please give a conclusion and prove it separately. (3) As shown in Figure ③, when 00 < α < 600, please draw a picture in the figure and point out that the quantitative relationship between ∠DME, ∠AEM and α is. (Just write the conclusion directly without proof) Figure ① Figure ② Figure ③ 17 As shown in the figure, in the known coordinate plane, straight lines l 1: y=x, L2: y = kx+4 (-1< k <; 0) The intersection point B, the intersection point l 2, the Y axis is at point A, and the intersection point BC⊥AB, the X axis is at point C. y (1) is used to find the S quadrilateral AOCB (expressed by the formula containing K); L 1 A B l 2 C O x (2) try to judge whether it is a fixed value; If yes, determine the value; Otherwise, explain the reason. 18, as shown in the figure, isosceles trapezoid abcd, ABCD, diagonal AC⊥BD is at point P, point A is on the Y axis, and points C and D are on the X axis. (1) If BC = 10, A(0 (2) If BC =, AB+CD=34, find the analytical expression of the inverse proportional function of the image passing through point B; (3) As shown in the figure, there is a point Q on PD, which connects CQ, and the P span is PE⊥CQ to S, the DC span is E, the DC span is EF=DE, the F span is FH⊥CQ to T, and the PC span is H. When Q moves on PD, does it change (not coincide with P and D)? If it changes, find out the scope of the change; If not, look for its value. F A E B C D diagram 1.

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