Four straight sides, joined up

Four dots on a page. Join them in order. Do you always get a quadrilateral, a four-sided shape?

No. Some ways of joining the dots make two sides cross.

Rule: A quadrilateral needs three things.

• Sides that are straight — no curves, no bends.
• A path that is closed — the last side meets the first.
• No side that cuts through another.

Join the same four dots in a different order. Try top-left, bottom-right, top-right, bottom-left. Two sides now cross in the middle. That shape fails the third rule: no side cuts through another.

A dented shape has one corner pushed inwards. It is still a quadrilateral, because its sides do not cross.

Every corner is where two sides meet. So a quadrilateral always has four corners, to match its four sides.

Drag a dot until two sides cross. Then drag it back.

Try the lab to finish this lesson.