Quadrilateral ABCD≅LMNO≅STUV

Question

. If STUV
is a rectangle and diagonal SU¯¯¯¯¯¯¯=5 cm
, what is the length of diagonals AC¯¯¯¯¯¯¯¯
and BD¯¯¯¯¯¯¯¯
?

Answer 1

Since ABCD is congruent to LMNO and STUV, all corresponding sides and angles are congruent.

Since STUV is a rectangle, opposite sides are parallel and congruent. Since ABCD is congruent to STUV, it is also a rectangle. Therefore, opposite sides of ABCD are parallel and congruent.

We know that AC is a diagonal. In a rectangle, diagonals bisect each other and are equal in length. Therefore, AC is equal to half of the length of BD.

Since ABCD is a rectangle, opposite sides are parallel and congruent. Additionally, the length of AC is equal to the length of BD divided by 2.

Since SU is a diagonal of STUV, it is also equal to the length of AC. Therefore, SU is equal to the length of BD divided by 2.

Given that SU is 5 cm, we can solve for the length of BD:

5 = BD/2
10 = BD

Therefore, the length of BD is 10 cm.

Since AC is equal to half of the length of BD, AC is equal to 10/2 = 5 cm.

Therefore, the length of diagonals AC and BD is 5 cm.