## Elementary Geometry for College Students (6th Edition)

To show that MNPQ is an isosceles trapezoid, its enough to show the legs are congruent or pair of angle base are congruent or the diagonals are congruent. In our case, given that MN || PQ, we conclude that angle NMP congruent to angle MPQ ( alternate angles are congruent ). By theorem, $m\angle NMP = 1/2 arc MQ$ and $m\angle MPQ= 1/2 arc MQ$. Since both angles are congruent then by setting up an equality therefore MQ=NP.