Exploring Trapezoids

Move the blue points around to investigate the properties of a trapezoid.
What is the definition of a trapezoid? What properties do trapezoids have? What can you say about side lengths, angles, diagonals? Are there certain conditions that give special trapezoids certain properties?
1) Is an isosceles trapezoid a parallelogram? 2) Are opposite sides of an isosceles trapezoid congruent? If so, how many pairs? 3) Are opposite angles of an isosceles trapezoid congruent? 4) Do the diagonals of an isosceles trapezoid bisect EACH OTHER? 5) Does a diagonal of an isosceles trapezoid bisect a pair of opposite angles? 6) Are the diagonals of an isosceles trapezoid perpendicular? 7) Are the diagonals of an isosceles trapezoid congruent? 8) Does either diagonal of a isosceles trapezoid serve as a line of symmetry? If so, how many?