Kite

Elementary School

Definition

This refers to a quadrilateral with two congruent pairs of adjacent sides. This is the cause of difference between a kite and a parallelogram, whose pairs of congruents sides are opposite to each other rather than being adjacent. A kite's diagonals are perpendicular. It very much does look like a kite that one can fly at the beach, and that's what it was named after.

Worked examples

\(ABCD\) is a kite with \(AB = AD = 5\) and \(BC = DC = 8\)

Two pairs of adjacent sides are congruent, and the diagonals meet at right angles.

Diagonals \(AC\) and \(BD\) intersect at \(E\), so \(\angle AEB = 90^\circ\)

In every kite, the diagonals are perpendicular to each other.

Common mistakes

A kite with sides \(5, 5, 8, 8\) is also a parallelogram → A kite has adjacent congruent sides; a parallelogram has opposite congruent sides Kites and parallelograms are different because their equal sides are positioned differently.
All four sides of a kite are congruent → A kite has exactly two pairs of adjacent congruent sides If all four sides were equal, it would be a rhombus, not just a kite.
Both diagonals of a kite bisect each other → Only one diagonal (the axis of symmetry) bisects the other Unlike a parallelogram, a kite's diagonals do not both bisect each other.

Where you'll use it next

You'll use kites when studying quadrilateral classification, proving properties of special figures, calculating areas using diagonal formulas, and solving geometry problems involving perpendicular segments.

Found in 1 StudyPug lesson

Classifying Quadrilaterals: From Basics to Advanced Concepts

Grade 5 Math placeholder

Dive into the world of quadrilaterals! Discover how to identify and classify various 4-sided shapes, understand their unique properties, and apply your knowledge to real-world scenarios.

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