In parallelogram ABCD, side AB = 6 cm, angle BAD = angle BCD = 45 degrees Find the diagonal of the parallelogram.

1. Since in a parallelogram the angles located opposite each other are equal, the angle ВСD = angle BAD = 45 °.

2. Angle CBD = 45 ° according to the problem statement. In triangle BCD, both angles at the base BC are equal to 45 °.

Therefore, this triangle is isosceles and its sides BD and CD are equal.

3. СD = AB = 6 cm, since the opposite sides of the parallelogram are equal. Therefore, the side ВD, of the triangle ВСD, which is the diagonal of the parallelogram, is 6 cm.

Answer: the length of the diagonal of the parallelogram is 6 cm.