Kites
Overview
A kite is a quadrilateral built from two pairs of consecutive congruent sides, with opposite sides not congruent. Its diagonals are perpendicular, exactly one diagonal is bisected, and exactly one pair of opposite angles is congruent — in kite ABCD as drawn in the notes, ∠A ≅ ∠C, while the other pair of opposite angles is the pair being bisected by a diagonal. Like every quadrilateral, its interior angles add to 360°.
Vocabulary
- Kite
- A quadrilateral with two pairs of consecutive sides that are congruent, but with opposite sides not congruent.
- Consecutive Sides
- Two sides of a polygon that share a vertex — they are next to each other.
- Perpendicular Diagonals
- Diagonals that intersect at right angles. The diagonals of a kite are perpendicular, written AC ⊥ BD.
- Bisected Diagonal
- A diagonal that is divided into two congruent parts by the other diagonal. In a kite, exactly one diagonal is bisected.
Main Ideas
- A kite has two pairs of consecutive congruent sides; opposite sides are not congruent, which separates a kite from a rhombus.
- The diagonals of a kite are perpendicular.
- Exactly one diagonal of a kite is bisected by the other.
- Exactly one pair of opposite angles is congruent, and exactly one pair of opposite angles is bisected by a diagonal — and they are not the same pair.
- The interior angles of a kite add to 360°, like those of every quadrilateral.
- Because the diagonals are perpendicular, each diagonal splits the kite into right triangles, so lengths along the diagonals can be found with the Pythagorean Theorem.
Lesson Notes
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