Reshape a shape freely with the sliders. Even as the size and angles keep changing, see for yourself that the properties unique to each shape — matching side lengths, matching angles, relationships between diagonals — never change.
A parallelogram is a quadrilateral where both pairs of opposite sides are parallel. From this one condition alone, a whole string of properties follows: "opposite sides are equal in length," "opposite angles are equal in size," and "the two diagonals bisect each other." Add one more condition at a time and you get an even more special shape. Make all four angles 90° and you get a rectangle (whose diagonals also become equal in length); make all four sides equal in length and you get a rhombus (whose diagonals meet at a right angle); satisfy both conditions at once and you get a square.
An isosceles triangle works similarly. From the single condition that two sides are equal in length, the two base angles opposite those sides automatically become equal too. Change the size or angle however much you like with the sliders, and check for yourself that these properties, fixed for each shape, never change.