Vertex
Grade 4 students learn that each corner of a polygon is called a vertex (plural: vertices) in Saxon Math Intermediate 4. The number of vertices always equals the number of sides — a pentagon has 5 sides and 5 vertices, an octagon has 8 of each. When a hexagon and pentagon are joined along one common side, the two shared vertices merge, giving 6 + 5 minus 2 = 9 total vertices. Students also learn the singular-plural distinction: one vertex, two or more vertices. This Chapter 7 skill develops precise geometric vocabulary essential for describing and classifying polygons.
Key Concepts
Each corner of a polygon is called a vertex (plural: vertices). A polygon has as many vertices as it has sides. This one to one relationship is a fundamental property of all simple polygons, making it easy to determine one count if you know the other.
A pentagon has 5 sides, so it must also have 5 vertices where the sides meet. An octagon has 8 sides and 8 vertices. A triangle has 3 sides and 3 vertices. So, an octagon has $8 3 = 5$ more vertices than a triangle. A decagon (10 sides) has 10 vertices, while a hexagon (6 sides) has 6 vertices. The decagon has 4 more.
Think of vertices as the 'pointy bits' or corners where the sides of a polygon meet up. They are the joints that hold the entire shape together. The coolest part is that there's a perfect one to one match: if you know the number of sides a polygon has, you automatically know it also has that exact same number of vertices.
Common Questions
What is a vertex in geometry?
A vertex is a corner of a polygon — a point where two sides meet. The plural of vertex is vertices. Every polygon has the same number of vertices as it has sides.
How many vertices does a hexagon have?
A hexagon has 6 sides, so it also has 6 vertices. In any simple polygon, the number of sides always equals the number of vertices.
How do you count vertices when two polygons share a side?
Add the vertices of both polygons, then subtract 2 for the shared vertices that merge into one. A hexagon (6 vertices) joined to a pentagon (5 vertices) along one side gives 6 + 5 minus 2 = 9 vertices in the combined shape.
What is the difference between vertex and vertices?
Vertex is singular — one corner point. Vertices is plural — two or more corner points. This distinction matters when writing geometry answers and using proper mathematical language.
What Saxon Math chapter covers the term vertex?
The concept of vertex and vertices is covered in Saxon Math Intermediate 4, Chapter 7 (Lessons 61-70), as part of studying polygon properties and geometric vocabulary.