There is a little E in the quadrilateral ABCD,

There is a little E in the quadrilateral ABCD,

Brother as like as two peas, the same thing is done by CAD. But ABE is not an equilateral triangle.
I can give you the picture,

In trapezoidal ABCD, AD / / BC, point E is on diagonal BD, and angle DCE = angle ADB. If BC = 9, CD / BD = 2 / 3, the length of CE is obtained

Angle ADB = angle DBC
And because angle ADB = angle DCE
Angle BDC = angle CDE
It can be concluded that the triangle BDC is similar to the triangle CED
So CD / BD = CE / CB = 2 / 3
CB=9
CE = 6

It is known that, as shown in the figure, in the quadrilateral ABCD, BD ⊥ CD, ∠ DAB = ∠ DBC = 45 ° and the area of △ ABC = 4.5, then the length of AB is______ ．

Make de through point D, perpendicular to ad, intersect the extension line of AB at point E, and connect CE. As shown in the figure, then △ DAE is isosceles right triangle,  2 = 45 °, ∨ BD ⊥ CD, ∠ DAB = ∠ DBC = 45 °, and 〈 DBC is also isosceles right triangle. In △ abd and △ ECD, ad = ed ∠ ADB = ∠ edcbd = CD, ≌ abd ≌ ECD, ≌ 1 = ∠ DAB = 45 °, ≌ CEB = 90 °, and 〈 CE is high, and CE = AB, 〈 triangle Form area = 12ab × CE = 12ab2 = 4.5, ab = 3, so the answer is: 3