In a rectangular trapezoid ABCD, the angles C and D are straight, the diagonal BD is the bisector of the angle D

In a rectangular trapezoid ABCD, the angles C and D are straight, the diagonal BD is the bisector of the angle D, AB = BD, AD = 2. a) Prove that the triangle BCD is isosceles, b) Prove that the triangle ABD is rectangular, c) Calculate the area trapezoid ABCD.

Since AB = BD, then A = 45 ° and the triangle ABD is rectangular and isosceles. It is easy to prove that the triangle BCD is a right-angled isosceles.
Moreover, BD = √2, a CD = 1. Therefore, the area of the trapezoid is 1.5.

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