Final answer:
The student is asked to draw a quadrilateral with perpendicular and equal diagonals, which is a square. The sketch should feature two perpendicular diagonals intersecting at their midpoints, with equal length sides creating right angles.
Step-by-step explanation:
The question asks for a sketch of a quadrilateral whose diagonals are perpendicular and equal in length. Such a quadrilateral is a square because the only quadrilateral that satisfies these properties, with both pairs of opposite sides being equal and parallel, and with diagonals that bisect each other perpendicularly and are of equal length, is a square.
To sketch this quadrilateral, begin by drawing two perpendicular lines that intersect at their midpoints. These will be the diagonals of the square. Next, draw four equal length lines connecting the endpoints of the diagonals to form a square. Ensure all internal angles are right angles, indicating that the sides are perpendicular to each other.