ABCD is an isosceles trapezoid 6. Given tow lines cut by a transversal, if one pair of interior angles on the same side as the transversal are supplementary the lines are parallel. My name is Erin O'Connor. I attend 8th grade at Saint Michael School in Olympia, Washington. By definition of an isosceles trapezoid, one pair of opposite sides is congruent and the other pair is not.
Opposite angles are supplementary, also by definition of a isosceles trapezoid.
Segments AB and DC are not congruent. Angle A and angle C are supplementary. If you use the theorem, if two interior angles on the same side of the transversal are supplementary, then the lines are parallel. That means the segment AB is parallel to segment DC, and that shows that quadrilateral ABCD is a trapezoid. Since segment AD is congruent to segment BC, the trapezoid must be isosceles.