In an isosceles trapezoid, the diagonal is equal to the larger base, and the angle at the base is 72

In an isosceles trapezoid, the diagonal is equal to the larger base, and the angle at the base is 72 degrees. Prove that the sides are equal to the smaller base.

Since, by condition, AC = AD, then the ACD triangle is isosceles, and therefore the angle ACD = ADC = 72.

Then the angle CAD = 180 – 72 – 72 = 36.

Since the angles at the base of an isosceles trapezoid are equal, the angle BAD = ADC = 72.

The angle BAC = BAD – CAD = 72 – 36 = 36, then AC is the bisector of the angle BAD.

Since the bisector of the trapezoid angle cuts off the segments equal to the lateral side at the base, AB = BC, and therefore CD = BC, which was required to be proved.