In a rectangular trapezoid, one of the corners is 45 degrees. The smaller side is equal
September 8, 2021 | education
| 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.
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