In a rectangular trapezoid ABCD (angle D – straight), the diagonal BD

In a rectangular trapezoid ABCD (angle D – straight), the diagonal BD is the bisector of the angle ABC, and the angle BAD is 60 °. Find the base of the trapezoid if the side AB is 6cm

Since, according to the condition, BD is the bisector of the angle, then the angle CBD = ABD.

The angle CBD = ADB as the cross-lying angles at the intersection of parallel lines CB and AD of the secant BD, then the angle ABD = ADB, which means that the triangle ABD is isosceles, AB = AD = 6 cm.

And since the angle ABD = 60, then triangle ABD is equilateral and its height BH is also the bisector and median of the triangle, then DH = AH = AD / 2 = 6/2 = 3 cm.

Quadrangle BCDH is a rectangle, then BC = DH = 3 cm.

Answer: The bases of the trapezoid are 3 cm and 6 cm.