In a rectangular trapezoid, one of the corners is 45 degrees. The smaller side is equal

In a rectangular trapezoid, one of the corners is 45 degrees. The smaller side is equal to the base. Prove that the grounds relate as 1: 2.

Let’s draw the height of the trapezoid CH. The formed quadrangle ABCN is a rectangle, since AB and CH are perpendicular to the bases of the trapezoid, and since, by condition, AB = BC, then ABCН is a square.

AB = BC = CH = AН.

In a right-angled triangle CDH, one of the acute angles is 45, then the triangle CDH is isosceles, CH = DH.

Then AD = AH + DH, and since AH = DH = BC, then AD = 2 * BC.

Then BC / AD = BC / 2 * BC = 1/2, which was required to prove.