As shown in the figure, in the isosceles trapezoid ABCD, the upper bottom AD= 12cm, the lower bottom BC= 14cm, the moving point P moves from point A to point D at the speed of 1cm/s along the edge of AD, and the moving point Q moves from point C to point B at the speed of 3cm/s along the edge of CB.

When do you take (1)t, and the quadrilateral PQCD is a parallelogram?

(2) When t is taken, is the quadrilateral PQCD an isosceles trapezoid?

Solution: (1) According to the problem, Q needs to move from C 14÷3≈4.67s, and P needs to move from A to D 12÷ 1= 12s.

? When point Q moves to point B, point P stops moving. And t≤4.67.

It can be known that AP=t, CQ=3t,

∴PD= 12-t,BQ= 14-3t

If the quadrilateral PQCD is a parallelogram, we can know that PD=CQ.

∴ 12-t=3t

∴t=3(s)

(2) If the quadrilateral PQCD is an isosceles trapezoid, then ∠ PQC = ∠ C.

In the isosceles trapezoid ABCD, ∠B=∠C, AD∨BC.

∴∠PQC=∠B

∴AB∥PQ

∴ Quadrilateral ABQP is a parallelogram.

∴AP=BQ

∴t= 14-3t

∴t=3.5(s)