In a simple polygon (a closed shape made of straight lines that don't cross each other), the number of sides and vertices are always equal.

Here's why:

* Vertex: A vertex is a corner point where two sides meet.

* Side: A side is a straight line segment connecting two vertices.

Every time you add a side to a polygon, you also create a new vertex where that side meets the previous one. This creates a one-to-one correspondence between sides and vertices.

Example:

* A triangle has 3 sides and 3 vertices.

* A quadrilateral has 4 sides and 4 vertices.

* A pentagon has 5 sides and 5 vertices.

This relationship holds true for all simple polygons, no matter how many sides they have.