Properties of kites

Definition of a Kite

  • A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal in length.

Properties of Sides

  • Two pairs of adjacent sides are congruent (equal in length).
  • Opposite sides are generally not equal.

Properties of Angles

  • One pair of opposite angles (between the unequal sides) is equal.
  • The other pair of opposite angles are generally unequal.

Diagonals of a Kite

  • The diagonals of a kite intersect at right angles (90°).
  • One diagonal bisects the other (the longer diagonal cuts the shorter diagonal into two equal halves).

Symmetry

  • A kite has one line of symmetry along the longer diagonal.
  • It does not have rotational symmetry of order more than 1.

Area of a Kite

  • The area is given by the formula:

Area = 1/2 × d1 × d2

Perimeter of a Kite

  • The perimeter is given by:

P = 2 (a + b)

Special Cases

  • If all four sides of a kite are equal, it becomes a rhombus.
  • If a kite has a right angle, it is called a right kite.

Real-life Examples

  • A flying kite, certain logos, and some architectural designs resemble the shape of a mathematical kite.

Learn with an example

Quadrilateral HIJK is a kite. What is ∠J?

∠J= _____°

∠H and ∠J are opposite angles. Also, ∠I and ∠K are opposite angles.

Since HIJK is a kite and ∠I≠∠K, ∠H=∠J. Use the fact that the sum of the interior angle measures of a quadrilateral is 360° to set up an equation and solve for ∠J.

∠H + ∠I + ∠J + ∠K = 360°

∠J + ∠I + ∠J + ∠K = 360° Substitute ∠H = ∠J

2 . ∠J + ∠I + ∠K = 360° Combine like terms

2 . ∠J + 138° + 130° = 360° Plug in ∠I = 138° and ∠K = 130°

2 . ∠J + 268° = 360° Combine like terms

2 . ∠J = 92° Subtract 268° from both sides

∠J = 46° Divide both sides by 2

So, ∠J=46°.

Quadrilateral RSTU is a kite. What is ∠U?

∠U= ____°

∠S and ∠U are opposite angles. Also, ∠R and ∠T are opposite angles.

Since RSTU is a kite and ∠R≠∠T, ∠S=∠U. Use the fact that the sum of the interior angle measures of a quadrilateral is 360° to set up an equation and solve for ∠U.

∠R+∠S+∠T+∠U = 360°

∠R+∠U+∠T+∠U = 360° Substitute ∠S=∠U

∠R+2∠U+∠T = 360° Combine like terms

72°+2∠U+46° = 360° Plug in ∠R=72° and ∠T=46°

2 . ∠U+118° = 360° Combine like terms

2 . ∠U = 242° Subtract 118° from both sides

∠U = 121° Divide both sides by 2

So, ∠U=121°.

🏋️‍♂️ Work it out🏋️‍♀️

Not feeling ready yet? These can help:

🥏Properties of parallelograms

Let’s practice!