This document discusses properties of trapezoids and kites. It defines a trapezoid as a quadrilateral with one pair of parallel sides, and an isosceles trapezoid as having congruent legs. Theorems state that in an isosceles trapezoid, the base angles are congruent and the diagonals are congruent. A midsegment connects the midpoints of the legs and equals half the sum of the parallel sides. A kite has two pairs of congruent adjacent sides, with perpendicular diagonals and one pair of congruent opposite angles. The document provides homework problems related to these shapes.