The diagonal of an isosceles trapezoid is perpendicular to the lateral side and lies on the bisector
| February 8, 2021 | education
The diagonal of an isosceles trapezoid is perpendicular to the lateral side and lies on the bisector of the acute angle of the trapezoid. Find angle with a larger base of the trapezoid.
Since, by condition, the ВD diagonal is perpendicular to AB, the AВD triangle is rectangular.
The trapezoid of AВСD is isosceles, then the angle ADС = ВAD, and since the diagonal of the ВD is also the bisector of the angle of AСD, then the angle ADВ = ВAD / 2.
In a right-angled triangle of AВD, the sum of the angles (ВAD + ADВ) = 90.
ВAD + ВAD / 2 = 90.
3 * ВAD = 180.
Angle ВAD = 180/3 = 60.
Answer: The angle for a larger base is 60.
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