Given an isosceles trapezoid ABCD (AD-greater base), its lateral sides are extended to the intersection at point O.

Given an isosceles trapezoid ABCD (AD-greater base), its lateral sides are extended to the intersection at point O. Prove that triangle OBC is isosceles.

According to the condition, the trapezoid of AВСD is isosceles, then AB = СD, and the angle ВAD = СDA.

In the ВOС triangle, the OBC angle is equal to the ВAD angle as the corresponding angles at the intersection of parallel straight lines BC and AD secant AO.

The ОСВ angle is equal to the ADС angle as well as the corresponding angles at the intersection of parallel BC and AD secant DO.

Since the angle ВAD = СDA, then the angle OBC = OCВ.

If in a triangle the angles at the base are equal, then such a triangle is isosceles, which was required to prove.