It is known that in diamond ABCD, e and F are points on AB and ad respectively, and AE = AF. verification: CE = CF

It is proved that ∵ ABCD is rhombic, ∵ ad = AB = BC = CD, ∵ d = ∵ B, AF = AE, ∵ FD = EB, ≌ DFC ≌ bec (SAS), ≌ CE = CF

In parallelogram ABCD, extend BC to P, extend DC to Q, so that CP / BC = CQ / DC = m, when s △ Apq = s ABCD, then M=

If CP / BC = CQ / DC, angle BCD = angle PCQ, then triangle BCD is similar to triangle PCQ, then PQ / BD = m (1), suppose triangle BCD, height on BD side is h, triangle PCQ, height on PQ side is h, then H / h = m, that is, H = MH, because parallelogram ABCD, then triangle Apq, height on PQ side is 2H + mhsabcd = BD * H (2), s △ Apq = 1 / 2pq * (2H + MH

RELATED INFORMATIONS

1. Given that ab = 1, CD = 2, the circumscribed sphere radius r = 3 in the tetrahedral ABCD, the maximum volume of the tetrahedral ABCD can be obtained
2. M ^ 2 + M-1 = 0, find the value of m ^ 3 + 2m ^ 2 + 2012
3. If the solution set of inequality | x2-8x + a | ≤ x-4 is [4,5], then the value of real number a is equal to______ ．
4. In triangle ABC, Pb is vertical to AB, PR is vertical to BC, PS is vertical to AC, and PQ = 6, PR = 8, PS = 10 Q. R and s are on three sides
5. In rectangular ABCD, the diagonal lines AC and BD intersect at O, ∠ AOD = 120 °, BC = 3cm under the root sign. Calculate the length of AC and the area of rectangular ABCD
6. The two diagonals of rectangle ABCD intersect at point O. given that the angle AOD is equal to 120 ° and ab is equal to 2.5cm, find the length of the diagonal of rectangle?
7. In rectangle ABCD, two diagonals intersect at point O, if ∠ AOD = 120 ° AB = 2, find the perimeter of rectangle
8. In rectangle ABCD, M is the midpoint of BC, Ma ⊥ MD. if the perimeter of rectangle is 48CM, the area of rectangle ABCD is______ cm2．
9. As shown in the figure, in rectangular ABCD, diagonal lines AC and BD intersect at point O, ∠ BOC = 120 ° AB = 6, find: (1) the length of diagonal line; (2) the length of BC; (3) the area of rectangular ABCD
10. The circumference of rectangle ABCD is 28cm, its two diagonals intersect at point O, the circumference of △ AOB is 2cm shorter than that of △ BOC, then AB = (), BC = ()
11. As shown in the figure, in △ ABC, D is the point on AB, DF intersects AC at e, de = Fe, AE = CE, what is the positional relationship between AB and CF? Prove your conclusion
12. Known: as shown in the figure, points B, e, C, f are on the same line, ab = De, AC = DF, be = CF
13. Known: as shown in the figure, points B, e, C, f are on the same line, ab = De, AC = DF, be = CF
14. As shown in the figure, ab = CD, DF ⊥ AC in F, be ⊥ AC in E, DF = be, verification: AF = CE
15. It is known that: as shown in the figure, AC bisects ∠ bad, CE ⊥ AB in E & nbsp; CF ⊥ ad in F, and BC = DC
16. As shown in the figure, ab | DC, ad | BC, points E and F are on AB and DC respectively, and be = DF, AF = CE
17. As shown in the figure, AC ⊥ BC, ad ⊥ BD, ad = BC, CE ⊥ AB, DF ⊥ AB, perpendicular feet are e and f respectively, so, CE = DF?
18. The vertical line CE is drawn from the vertex C of rectangle ABCD to the diagonal BD, and the perpendicular foot is e. if CE is divided into two angles with ∠ C being 1:5, then ∠ ace=
19. It is known that in trapezoid ABCD, ab ∥ CD, ad = DC = BC = 4 ∠ DCB = 120 ° CE ⊥ AB, the area of AC ⊥ BC and trapezoid is calculated
20. Known: as shown in the figure, EF is the median line of trapezoidal ABCD, AF bisector angle DAB verification: ad = 2ef There is no picture