Quadrilaterals
35. Four-Sided Figures · Defining the quadrilateral family
It always remains a closed figure with 4 sides, 4 vertices, and 2 diagonals.
A quadrilateral is a closed figure with four sides, four vertices, and two diagonals. Common quadrilaterals include the rectangle, square, parallelogram, rhombus and trapezium.
What this lesson covers
Try to break it
Try to break it by dragging corners wildly. No matter how you stretch, you'll always have a closed shape with exactly four sides — that's the promise of a quadrilateral.
How you build it
Make a quadrilateral with diagonals.
- Place point A on the canvas — the first corner.
- Place point B — the second corner.
- Place point C — the third corner.
- Place point D — the fourth corner.
- Draw side AB joining points A and B.
- Draw side BC joining points B and C.
- Draw side CD joining points C and D.
- Draw side DA joining points D and A — this closes the quadrilateral.
- Draw diagonal AC joining the opposite corners A and C.
- Draw diagonal BD joining the opposite corners B and D.
The proof, step by step
Prove that the figure is a quadrilateral — four sides and four vertices.
- A quadrilateral always has exactly four sides.
- It has four vertices where the sides meet.
- Two diagonals connect opposite vertices inside the figure.
Worked example
A polygon has 4 straight sides and 4 vertices. Which of the following correctly classifies this shape?
By definition, a four-sided closed figure with four vertices is called a quadrilateral. Triangles have 3 sides, pentagons 5, and hexagons 6.
- Triangle
- Quadrilateral — correct
- Pentagon
- Hexagon