Since quadrilaterals ABCD, LMNO, and STUV are all congruent, they share the same properties, including the lengths of their diagonals.
Given that STUV is a rectangle and its diagonal \( SU = 5 , \text{cm} \), we can find the lengths of the other diagonal \( TV \) as well. In a rectangle, both diagonals are equal, so \( TV = SU = 5 , \text{cm} \).
For quadrilaterals that are congruent, the diagonals will also be congruent. Since ABCD and LMNO are congruent to STUV, the lengths of diagonals \( AC \) and \( BD \) (of quadrilateral ABCD) must also be equal to the lengths of diagonals \( SU \) and \( TV \).
Thus, according to the Transitive Property of congruence, we have:
\[ AC = BD = SU = 5 , \text{cm} \]
Therefore, the lengths of diagonals \( AC \) and \( BD \) are both \( 5 , \text{cm} \).
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