Kites - Interactive Activity

A kite is a quadrilateral with two pairs of consecutive congruent sides, but with opposite sides not congruent. These activities let you drag a kite into new shapes and watch its properties stay true, name the property a picture shows, and build complete solutions one step at a time.

Definitions and Main Ideas

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.

The Polygon Family Tree

Properties are inherited as we move down the tree. The highlighted shape, Kite, is the shape in this lesson.

Kite Explorer

What to do: Drag the orange handle at B or the purple handle at D to stretch the kite along its axis, or drag the dark cyan handle at A to make the kite taller or shorter. Point C is placed as the mirror image of A, so the figure is always a kite. Watch the readouts as you drag.

B and D slide along the axis, and A slides straight up and down. A move that would push the figure off the drawing area or make a part too short is not accepted. A move that would make the two pairs of sides equal is not accepted either — the figure would be a rhombus, not a kite.

Name the Property

What to do: Look at the marks and the values shown on each kite. Choose the property the picture shows. A first miss gives a hint and another try. The Next problem button cycles through all eight problems in order.

The Next problem button cycles through all eight problems in order.

Build the Solution

What to do: Work each problem one step at a time. Step 1 chooses the equation that should be used to solve the problem. A first miss gives a hint and another try. The gold highlight marks the part the current step asks about, and a part solved in an earlier step is labeled with its found value.

Continue moves to the next step. New problem cycles through all six problems in order.

Your Turn

What to do: Answer all six questions. A first miss gives a hint and another try; after a second miss the answer is shown and explained. Your score counts first-try answers only.

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Kites — Mr. J Geometry. All activities on this page run entirely in your browser.