Answer: Second diagram and fourth diagram.
Step-by-step explanation:
A kite is a quadrilateral which has two pairs of congruent adjacent sides.
In diagram 1:
By the distance formula,
The sides of the given quadrilateral are \(\sqrt{a^2+c^2}\), \(\sqrt{b^2+c^2}\), \(\sqrt{b^2+d^2}\) and \(\sqrt{a^2+d^2}\)
Since, here a, b, c and d are unknown numbers,
Thus, this quadrilateral does not have any pair of congruent adjacent sides.
⇒ It is not a kite.
In diagram 2:
By the distance formula,
The sides of the given quadrilateral are \(a\), \(a\sqrt{5}\), \(a\sqrt{5}\) and \(a\)
Since, this quadrilateral has two pairs of congruent adjacent sides.
⇒ It is a kite.
In diagram 3:
By the distance formula,
The sides of the given quadrilateral are \(a\), \(\sqrt{b^2+(c-a)^2}\), \(\sqrt{(b-a)^2+c^2}\) and \(a\)
Since, here a, b, c and d are unknown numbers,
Thus, this quadrilateral only have only one pair of congruent adjacent sides.
⇒ It is not a kite.
In diagram 4:
By the distance formula,
The sides of the given quadrilateral are \(\sqrt{b^2+c^2}\), \(\sqrt{b^2+c^2}\), \(\sqrt{a^2+c^2}\) and \(\sqrt{a^2+c^2}\)
Since, this quadrilateral has two pairs of congruent adjacent sides.
⇒ It is a kite.
