Question

given three distinct quadrilaterals, a square, a rectangle, and a rhombus, which quadrilaterals must have perpendicular diagonals

Answer 1

Which ones are perpendicular?

Answer 2

oh ok

Answer 3

the second

Answer 4

Nope.
Remember that perpendicular means that the angle between the two is 90 degrees.
Since the diagonals cross, the angles between all sides must the same for the the angle to be 90 degrees.

Answer 5

In the case of the rectangle,

Angles A and B are equal and angles C and D are equal, but none of the 4 angles are 90 degrees.