Topic: In trapezoidal ABCD, AB and CD are parallel, with an included angle of A=90 degrees, DC= 12cm, AD=9cm, AB= 18cm. The moving point P starts from D and moves to point C at a speed of 1cm per second, while the moving point Q starts from point B and moves to point 3cm per second.

When is the value of (1)t and why is the quadrilateral PQBC a right trapezoid?

(2) Why is the quadrilateral PQBC an isosceles trapezoid when t is a value?

(1) when DP=AQ, the quadrilateral PQBC is a right trapezoid; By DP= 1*t, AQ=AB-BQ=AB-3*t= 18-3t, if DP=AQ, t= 18-3t, t=4.5 (seconds);

(2) When the quadrilateral PQBC is trapezoidal, one side waist is fixed as BC; When it is an isosceles trapezoid, the difference between the distance q from point P to line DA and the distance to line AD should be equal to the difference between side lengths BA and DC; That is, t-(18-3t) =18-12, ∴ t=6 (seconds);