Derek D. answered • 06/12/20
Extensive experience in public education, B.A.S in math gr 5-9
Definitions are very important when concerning these great questions. Recall:
a) A rhombus is a special kind of parallelogram, where all the sides are congruent.
b) A square is a special kind of rhombus, where all the angles are congruent (to 90°).
We know a square is a parallelogram with congruent sides and congruent angles, and has diagonals that are congruent and perpendicular. Therefore, only in some cases, a parallelogram can have diagonals that are both congruent and perpendicular (like squares).
It is important to emphasize that all squares are rhombuses, but not all rhombuses are squares- to address your example of a rhombus with congruent diagonals, implies that the rhombus must be a square for it's diagonals to be congruent.
