The total of the measures of the internal angles of a quadrilateral is 360 degrees.
So, if all four internal angles of a quadrilateral are equal, they must all be 90 degree angles. So the quadrilateral must be either a rectangle or a square.
Rectangles and squares are parallelograms.
Sufficient.
Statement 2:
This seems sufficient, because a diagonal of a parallelogram divides the parallelogram into two congruent triangles, but check out what you can do.
You can create a quadrilateral two halves of which are mirror images of each other while the quadrilateral is not a parallelogram.
Insufficient.
The correct answer is A.
