Let the parallel line with point C as AD intersect with the extension line of BA at point E, first prove that the quadrilateral ADCE is a parallelogram, and get CD=AE, CE=AD=6, and then prove CE⊥BC. Then, according to Pythagorean theorem, get BE2=BC2+CE2= 100, and then get AB+.

answer

Solution: As shown in the figure, point C is the parallel line of AD, and the extension line of intersection BA is at point E. 。

∫AB∨CD，CE∨AD，

The quadrangle is a parallelogram,

∴CD=AE,CE=AD=6.

∵AD⊥BC,CE∥AD，

∴CE⊥BC，

∴BE2=BC2+CE2=82+62= 100，

∴BE= 10，

∴AB+CD=AB+AE=BE= 10.