Quadrilateral ABCD≅LMNO≅STUV

Question

. If STUV
is a rectangle and diagonal SU¯¯¯¯¯¯¯=5 cm
, what is the length of diagonals AC
and BD
?(1 point)
According to the Transitive Property, AC
and BD=
cm.

Answer 1

Since quadrilaterals ABCD and LMNO are congruent to STUV, which is a rectangle, we can conclude the following about the diagonals.

In a rectangle, the diagonals are equal in length. Therefore, the length of diagonal \( SU \) in rectangle \( STUV \) is 5 cm. By the property of congruence:

• Since \( ABCD \cong STUV \), the lengths of the corresponding diagonals \( AC \) and \( BD \) in quadrilateral \( ABCD \) must also be equal to the length of the diagonals in rectangle \( STUV \).

Thus, by the Transitive Property, we can state:

\[ AC = BD = SU = 5 \text{ cm} \]

So, the lengths of diagonals \( AC \) and \( BD \) are both 5 cm.