Fundamental Concepts
6. Open vs. Closed · Where do the lines meet?
The figure closes completely when P meets F, enclosing an area.
A closed figure has its boundary connect back to its starting point — it encloses a region. An open figure has a gap somewhere along its boundary. Drag P toward F to close the figure.
What this lesson covers
Try to break it
When P is away from F, the figure is OPEN. It doesn't trap any space inside—it has a gap!
How you build it
Make a closed figure.
- Place point A (start of the figure).
- Place point B.
- Draw segment AB.
- Place point C.
- Draw segment BC.
- Draw segment CA back to the start. Now the figure is closed.
The proof, step by step
Prove that the figure is closed — its boundary meets end to end.
- A closed figure is bounded by continuous curves or lines.
- The curves or lines do not intersect each other.
- The start and end points meet, enclosing an area.
- An open figure does not enclose an area and has a gap.
Worked example
Which of the following statements correctly describes a closed figure?
A closed figure is bounded by continuous curves or lines that meet at the start and end point, enclosing an area without any gaps.
- It has a gap and does not enclose space.
- It is bounded by continuous lines that meet at the start and end. — correct
- It always has curved sides only.
- It intersects itself at multiple points.