Triangles
93. The Three-Sided Promise · Always closed, always three sides
A triangle always has exactly 3 sides and 3 vertices.
A triangle is a closed figure with 3 vertices, 3 sides, and 3 interior angles. The simplest polygon — three non-collinear points are always enough to define one and only one triangle.
What this lesson covers
Try to break it
Drag the corners A, B, and C. Watch how the sides stretch and the angles change, but it always stays a triangle with three sides.
How you build it
Make a triangle.
- Place the first point A anywhere on the canvas.
- Place the second point B.
- Place the third point C.
- Draw a line connecting A and B.
- Draw a line connecting B and C.
- Draw a line connecting C and A to close the figure.
The proof, step by step
Prove that the figure is a triangle — three sides and three vertices.
- A triangle is a closed figure formed by three line segments.
- The three points where the sides meet are called vertices.
- A triangle has exactly three sides, three angles, and three vertices.
- These three sides and three angles are known as the six elements of a triangle.
Worked example
A closed plane figure bounded by three line segments is called a:
By definition, a closed figure with exactly three sides is a triangle. It has three vertices and three angles.
- Quadrilateral
- Triangle — correct
- Polygon
- Circle