Prove that in an isosceles trapezoid: a) the angles at each base are equal, b) the diagonals are equal

An isosceles trapezoid is a trapezoid in which the sides are equal. Consider the AВСD trapezoid. Lateral side AB = СD. Opposite these sides lie angle D and angle A, which are also equal, since they lie opposite to equal sides. Angle B is one-sided corner A, corner C is one-sided corner D. One-sided angles add up to 180 degrees. Angle B = 180 – angle A. Angle C = 180 – angle D. Answer a) The angles are equal.
Let’s draw the diagonals AC and ВD. Consider triangle ABC and triangle AСD. The diagonal AC lies opposite the angle D, and the diagonal ВD is opposite the angle A. Angle A = D, which means AC = ВD. Answer b) The diagonals are equal.