Triangles
24. Where Sides Meet · Discover the vertices of a triangle
The vertices are always the points where two sides meet.
A vertex of a triangle is a corner point where two sides meet. A triangle has three vertices, usually labelled A, B and C.
What this lesson covers
Try to break it
What if we pull a point so the sides don't meet? Try dragging A far away. The sides still meet at A, but the triangle gets stretched. A vertex is always where two sides meet, even if the triangle looks weird!
How you build it
Make a triangle and find its vertices.
- Place vertex A.
- Place vertex B.
- Place vertex C.
- Draw side AB.
- Draw side BC.
- Draw side CA. A, B, C are the vertices — each is a meeting point of two sides.
The proof, step by step
Prove a triangle has three vertices.
- A vertex is defined as the point where two sides of a triangle meet.
- Since a triangle has three sides, there are three pairs of intersecting sides.
- Therefore, every triangle has exactly three vertices.
Worked example
In triangle XYZ, which points are the vertices?
Vertices are the points where sides meet. In triangle XYZ, the sides meet at points X, Y, and Z.
- X, Y, and Z — correct
- XY, YZ, and ZX
- Only X
- The midpoints of the sides