Answer:
Square.
Step-by-step explanation:
The parallelogram that has those characteristics is the square.
The square is perfectly symmetric, both diagonals are congruent, because all sides of the square are congruent. Also, the diagonals bisects each angle of the square, creating triangles. Those triangles have 45° angles at their base and the third-angle is 90°, that is, it's a right triangle, where that right angle is between diagonals.
Therefore, a square has congruent and perpendicular diagonals, they have the same midpoint, and their slopes are opposite reciprocals of each other because that's the definition of perpendicularity.
Therefore, the right answer is square.
