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Quadrilateral labeled with vertices upper A, upper B, upper C, and upper D. The segment between upper B and upper D is longer than the diagonal between upper A and upper C.

In quadrilateral ABCD , BC=8 , and CD=12 . To prove that the quadrilateral is a kite, what must be the length of AD¯¯¯¯¯¯¯¯ ?

(1 point)
The length of AD¯¯¯¯¯¯¯¯ is
.

1 answer

In a kite, the two pairs of adjacent sides are equal in length. Since we are given that \( BC = 8 \) and \( CD = 12 \), we need to find \( AD \) such that \( AD \) is equal to \( AB \).

For quadrilateral \( ABCD \) to be a kite, we require:

  1. \( AB = AD \)
  2. \( BC = CD \)

However, we do not have \( AB \) given directly.

But from the properties of a kite, we can infer that in this case, if one pair of opposite sides (defined by the lengths) must also lead to the equality between the other side length.

Thus, we conclude that if \( BC = 8 \) and to satisfy the kite property, we would need \( AD \) to also be equal to \( 12 \).

So, to fulfill the condition of \( AD \) being equal to the other side adjacent \( CD \), we assume it can equal \( 12 \).

Therefore, for quadrilateral \( ABCD \) to be a kite,

The length of \( \overline{AD} \) is \( 12 \).