Answer :
Final answer:
Polygon IJKL, having equal opposite sides and angles, with two pairs of parallel sides, is described as a parallelogram and a quadrilateral. Therefore the correct option is ( A .
Explanation:
The given information about the polygon IJKL allows us to describe its properties. We are given that IJ=23, JK=46, KL=23, LI=46, which indicates that opposite sides are equal. Additionally, it's mentioned that ∠I ≅ ∠K, and ∠J ≅ ∠L, suggesting that opposite angles are congruent. The conditions IJ∥∥KL and JK∥∥LI show us that opposite sides are parallel. With these properties, the polygon can be described as a parallelogram. Since not all angles are mentioned to be right angles, it cannot be identified as a rectangle. As the lengths of the sides are not all equal, it is also not a rhombus or a square. The definition of a quadrilateral is a polygon with four sides, which applies here. Finally, a trapezoid has only one pair of parallel sides, so this does not describe IJKL since it has two pairs of parallel sides.