In trapezoid ABCD, the midpoint ad ‖ BC, ab = ad = DC = 5, cos ∠ ABC = 3 / 5, e is the midpoint of edge AB, and point F is the first moving point of ray BC, connecting BD and DF (1) Finding Tan angle abd when DF is perpendicular to BC (2) When point F is on the extension line of BC, connect EF with DC at point G, let CF be equal to m, and find the length of line segment DG (expressed by the algebraic expression containing m) (3) Let m be a point on DC and 5DM equal to 8ae. Join am to intersect diagonal BD at point n. if triangle BDF equals triangle and, find the length of segment CF

In trapezoid ABCD, the midpoint ad ‖ BC, ab = ad = DC = 5, cos ∠ ABC = 3 / 5, e is the midpoint of edge AB, and point F is the first moving point of ray BC, connecting BD and DF (1) Finding Tan angle abd when DF is perpendicular to BC (2) When point F is on the extension line of BC, connect EF with DC at point G, let CF be equal to m, and find the length of line segment DG (expressed by the algebraic expression containing m) (3) Let m be a point on DC and 5DM equal to 8ae. Join am to intersect diagonal BD at point n. if triangle BDF equals triangle and, find the length of segment CF

1. AB = ad, ∠ abd = ∠ ADB ∫ ad ∥ BC,  ADB = ∠ DBC ℅ abd = ∠ DBC = ∠ adbtanabd = Tan (1 / 2 ∠ ABC) = = = √ ((1-cosabc) / ((1 + cosabc)) = √ ((1-3 / 5) / ((1 + 3 / 5)) = 1 / 22, through point e to do en ⊥ BC, through point G to do GM ⊥ BC, through point a to do AP ⊥ BC, through point d to do DQ ⊥ BC, so