As shown in the figure, in the trapezoidal ABCD, DC ‖ AB, ad = BC, BD bisects ∠ ABC, a = 60 ° (1) find the degree of ∠ abd; (2) if ad = 2, find the length of diagonal BD

As shown in the figure, in the trapezoidal ABCD, DC ‖ AB, ad = BC, BD bisects ∠ ABC, a = 60 ° (1) find the degree of ∠ abd; (2) if ad = 2, find the length of diagonal BD

(1) ∵ DC ‖ AB, ad = BC, ∵ trapezoid ABCD is isosceles trapezoid, ∵ ABC = ∵ a = 60 °, and ∵ BD bisection ∵ ABC, ∵ abd = ∵ CBD = 12 ∵ ABC = 30 ° (2) ∵ a = 60 °, ∵ abd = 30 °, ∵ ADB = 90 °, ∵ AB = 2ad = 4, (the side of 30 ° in a right triangle is half of the hypotenuse) ∵