Make a kite

The idea

A kite is a quadrilateral that can be labelled ABCD such that AB = BC and CD = DA, that is, with two non-overlapping pairs of equal adjacent sides.

Two triangles, one new shape

Two identical triangles have sides 6 cm, 9 cm and 12 cm. Lay the second one over the first, then flip it over along the 12 cm side. The two triangles together make a four-sided shape.

Where will the equal sides of the new shape sit?

• Opposite each other, as in a parallelogram
• Next to each other, in two pairs
• All four sides are equal

Join the triangles

Choose which side to glue along, then flip the copy over it, or turn it half-way round. Look at where the equal sides sit. Can you make a kite and a parallelogram?

Equal neighbours

A kite is a quadrilateral that can be labelled ABCD such that AB = BC and CD = DA, that is, with two non-overlapping pairs of equal adjacent sides.

Flipped over the 12 cm side, the two 6 cm sides meet at one end of the glue line, and the two 9 cm sides meet at the other end. So AB = BC = 6 cm and CD = DA = 9 cm: the equal sides are neighbours, not opposite each other.

Why do they land side by side? The copy is a mirror image. At each end of the glue line, a side of the first triangle and the same side of the copy start from one point, and they are equally long.

The half-turn did the opposite: it put the equal sides opposite each other, and made a parallelogram.

"Non-overlapping" means the two pairs use four different sides: AB and BC in one pair, CD and DA in the other.

Flipping along a shorter side also gives two pairs of equal neighbours, but a corner can dent inwards like an arrowhead. The kite you know bulges at every corner. It comes from flipping along the longest side.

Notes

A kite is a quadrilateral that can be labelled ABCD such that AB = BC and CD = DA, that is, with two non-overlapping pairs of equal adjacent sides.

Check yourself

In quadrilateral ABCD, AB = BC = 5 cm and CD = DA = 3 cm. What is it?

In kite ABCD, AB = BC = 7 cm and CD = 4 cm. How long is DA?

Answer: 4 cm

A kite has two pairs of equal neighbours: AB = BC and CD = DA. So DA = CD = 4 cm.

Two identical triangles with sides 4 cm, 7 cm and 9 cm are glued along the 9 cm side, with the copy flipped over. What do they make?

A kite ABCD has AB = BC = 8 cm and CD = DA = 5 cm. What is the perimeter, in cm?

Answer: 26 cm

AB + BC + CD + DA = 8 + 8 + 5 + 5 = 26 cm.

• A kite — correct. Yes! AB = BC and CD = DA are two pairs of equal neighbouring sides.
• A parallelogram. In a parallelogram the equal sides are opposite each other. Here AB = 5 cm but CD = 3 cm.
• A rhombus. A rhombus has all four sides equal. These sides are 5 cm and 3 cm.
• A kite with sides 4, 4, 7, 7 cm in order — correct. Yes! The mirror copy puts the two 4 cm sides together at one end and the two 7 cm sides together at the other.
• A parallelogram with sides 4, 7, 4, 7 cm in order. That comes from turning the copy half-way round. Flipping puts the equal sides side by side.
• A rhombus. A rhombus needs all four sides equal. These sides are 4 cm and 7 cm.