Here's a brief overview of the main properties of an isosceles trapezoid:
The diagonals of an isosceles trapezoid are of equal length.
But these diagonals do not necessarily bisect each other.
The base angles are the same.
An isosceles trapezoid which is also a right trapezoid is a rectangle.
An isosceles trapezoid has an axis of symmetry - the line of symmetry goes through the midpoints of the bases.
But an isosceles trapezoid has no rotational symmetry (unless it is a rectangle).
The sum of opposite angles is equal to the straight angle (180 degrees).
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