Question

prove that the diagonals of the square bisect the interior angles

Answer 1

you have square ABCD, diagonal AC and the resulting triangle ABC to be isosceles.
because B is a right angle, it follows that angles CAB and ACB are the congruent base angles of the triangle ABC.
the congruent angles measure 45 degrees.
a similar reasoning on triangle ADC yields 45 degrees on angles ACD and CAD.

Answer 2

because DAC and BAC are both 45 degress, they are congruent and therefore the diagonal bisects the right angle DAB