3.3.2. Kite

Kite is a special type of a quadrilateral. The sides with the same markings in each figure are equal. For example AB = AD and BC = CD.

A kite is defined as a specific kind of quadrilateral. It has four sides, and it possesses a distinctive property where there are two pairs of adjacent sides that are equal in length. This can be expressed mathematically as AB = AD and BC = CD. This definition is fundamental as it distinguishes kites from other quadrilaterals that may not have this property.

Think of a kite you fly in the sky. When you look at its shape, you will notice that the two sides on one diagonal (let’s say the left and right sides of the kite) are the same length, while the other two sides (top and bottom) are also equal in length, but they look different. This resembles our definition of the sides being equal in pairs.

These are kites These are not kites Study these figures and try to describe what a kite is. Observe that (i) A kite has 4 sides (It is a quadrilateral). (ii) There are exactly two distinct consecutive pairs of sides of equal length. Check whether a square is a kite.

When studying kites, we can identify their characteristics more clearly. First, all kites are quadrilaterals, meaning they consist of four sides. Moreover, a kite is unique in that it has exactly two pairs of consecutive sides that are equal: this means that if you look at any two adjacent sides, they will be equal in length to each other. For example, if AB = AD, then these form one pair, while BC = CD forms the other pair. It’s important to note that a square, which has all sides equal, can be checked against these conditions to confirm if it fits the definition of a kite.

Imagine a diamond shape that you may see in jewelry. This shape can sometimes resemble a kite, especially in design, where you notice that two sets of sides are longer or shorter—just like a kite in shape and structure. To think of a square, just remember all four sides are equal—like a box—but remember that kites only require two pairs of consecutive equal sides.

DO THIS Show that ∆ABC and ∆ADC are congruent. Take a thick white sheet. Fold the paper once. Cut along the line segments and open up. What do we infer from this?

This activity demonstrates congruency in kites. By folding the paper in half, you can show that the two triangles formed (∆ABC and ∆ADC) are congruent. This means they are identical in shape and size. When you cut along the line segments and unfold the paper, you can see that both triangles match perfectly. This congruency is a valuable attribute because it shows symmetry in kites, particularly in relation to their diagonals, which intersect at right angles.

Consider how folding a piece of paper on a crease line creates two halves that are mirror images of each other. This is similar to how a kite acts when folded along its diagonal, helping to visually represent how the shape is balanced and symmetric. This can be likened to reflecting on a pond where the water is still, and you can see your image clearly—each side, like the two halves of a kite, reflects perfectly.

Has the kite any line symmetry? Fold both the diagonals of the kite. Use the set-square to check if they cut at right angles. Are the diagonals equal in length? Verify (by paper-folding or measurement) if the diagonals bisect each other. By folding an angle of the kite on its opposite, check for angles of equal measure. Observe the diagonal folds; do they indicate any diagonal being an angle bisector?

Kites exhibit distinctive properties related to their diagonals. One key feature is that kites have one line of symmetry, which runs along the line where the unequal angles are found. When you fold the diagonals, they intersect at a right angle, revealing that one diagonal (the longer one) bisects the other. This means that the shorter diagonal is divided into two equal parts at the intersection. Additionally, angles adjacent to this diagonal will be equal, emphasizing the kite's unique symmetry and structure.

Imagine playing with an actual kite. When you string it up, the main frame creates a sort of 'spine' along which the fabric is symmetrical. If you visualize cutting that kite along its spine to see each side match perfectly, you've envisioned splitting it right down the line where the diagonals cross—it helps show how kites balance and fly gracefully in the wind.

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