Choose ALL answers that describe the quadrilateral \( E F G H \) if \( \overline{E F}\|\overline{G H}, \overline{F G}\| \overline{H E}, E G=F H \), and diagonals are perpendicular: \( \overline{E G} \perp \overline{F H} \).

To solve this problem, let's analyze the given conditions and deduce the properties of quadrilateral \( E F G H \). 1. \( \overline{E F} \parallel \overline{G H} \) and \( \overline{F G} \parallel \overline{H E} \): This means that opposite sides of the quadrilateral are parallel, which is a characteristic of a parallelogram. 2. \( E G = F H \): This condition indicates that the diagonals of the quadrilateral are of equal length. 3. \( \overline{E G} \perp \overline{F H} \): The diagonals are perpendicular to each other. Based on these conditions, we can deduce the following about quadrilateral \( E F G H \): - It is a parallelogram because it has two pairs of parallel sides. - It is a rectangle because it has equal diagonals and perpendicular diagonals. In a parallelogram, if the diagonals are perpendicular and of equal length, then the parallelogram is a rectangle. Now, let's choose the correct answers from the given options: 1. It is a parallelogram. 2. It is a rectangle. 3. It has equal diagonals. 4. It has perpendicular diagonals. All of these statements are true based on the given conditions. Therefore, the correct answers are: - It is a parallelogram. - It is a rectangle. - It has equal diagonals. - It has perpendicular diagonals.