#### Answer

1. Since DC is the midpoint of the isosceles triangle, it is parallel to the base, which is AB.
2. Since these two sides are parallel and there are 4 sides total, ABCD is a trapezoid.
3. Since DC is the midpoint of the isosceles triangle AEB, it follows that AD is congruent to CB.
4. Since the opposite sides of the trapezoid are congruent, the trapezoid is an isosceles trapezoid.