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

Given that quadrilateral \( ABCD \) is congruent to \( LMNO \) which is congruent to \( STUV \), and that \( STUV \) is a rectangle with a diagonal \( SU = 5 , \text{cm} \):

In a rectangle, the diagonals are congruent. Thus:

• \( SU = TV = 5 , \text{cm} \)

Since \( STUV \) is congruent to \( ABCD \), the lengths of the diagonals \( AC \) and \( BD \) in quadrilateral \( ABCD \) are also equal to \( 5 , \text{cm} \).

According to the Transitive Property:

• \( AC = BD = 5 , \text{cm} \)

Thus, the lengths of diagonals \( AC \) and \( BD \) are: \[ AC = BD = 5 , \text{cm} \]