As shown in the figure, in trapezoidal ABCD, ad ‖ BC (BC > AD), ∠ d = 90 °, BC = CD = 12, ∠ Abe = 45 °, if AE = 10, the length of CE is______ ．

As shown in the figure, in trapezoidal ABCD, ad ‖ BC (BC > AD), ∠ d = 90 °, BC = CD = 12, ∠ Abe = 45 °, if AE = 10, the length of CE is______ ．

Through B, make the vertical line of Da intersect with the extension line of DA at m, M is the vertical foot, extend DM to g, make mg = CE, connect BG, it is easy to know that the quadrilateral BCDM is a square, so BC = BM, ∠ C = ∠ BMG = 90 °, EC = GM, ≌ BEC ≌ BMG (SAS), ≌ MBG = ∠ CBE, ∫ Abe = 45 °, ∫ CBE + ∠ ABM = 45 °, ≌

As shown in the figure, in trapezoidal ABCD, ad ‖ BC (BC > AD), ∠ d = 90 °, BC = CD = 12, ∠ Abe = 45 °, if AE = 10, the length of CE is______ ．

Through B, make the vertical line of Da intersect with the extension line of DA at m, M is the vertical foot, extend DM to g, make mg = CE, connect BG, it is easy to know that the quadrilateral BCDM is a square, so BC = BM, ∠ C = ∠ BMG = 90 °, EC = GM, ≌ BEC ≌ BMG (SAS), ≌ MBG = ∠ CBE, ∫ Abe = 45 °, ∫ CBE + ∠ ABM = 45 °, ≌

As shown in the figure, in trapezoidal ABCD, ad is parallel to BC (BC > AD), angle d = 90 degrees, BC = CD = 12, and angle Abe = 45 degrees. If AE = 10, calculate the length of CE

Make the extension line of BM perpendicular to DA at m, then the quadrilateral MBCD is a square. Extend DC to N, so that CN = ma, connect BN. Then BM = BC, ∠ BMA = ∠ BCN = 90 °, then ≌ Δ BCN (SAS) · BN = Ba; and ∠ CBN = ∠ MBA. Then ∠ CBN + ∠ CBE = ∠ MBA + ∠ CBE = ∠ MBC - ∠ Abe = 45 degrees, that is ∠ NBE = ∠ Abe; and be = be

As shown in the figure, in trapezoidal ABCD, ad ‖ BC (BC > AD), ∠ d = 90 °, BC = CD = 12, ∠ Abe = 45 °, if AE = 10, the length of CE is______ ．

Through B, make the vertical line of Da intersect with the extension line of DA at m, M is the vertical foot, extend DM to g, make mg = CE, connect BG, it is easy to know that the quadrilateral BCDM is a square, so BC = BM, ∠ C = ∠ BMG = 90 °, EC = GM, ≌ BEC ≌ BMG (SAS), ≌ MBG = ∠ CBE, ∫ Abe = 45 °, ∫ CBE + ∠ ABM = 45 °, ≌