Difference Between Vertex and Vertice in Geometry
Vertex Definition plays a key role in geometry and algebra. You’ll often need to spot vertices when answering questions about shapes, angles, or graphs in CBSE and competitive exams. Mastering this idea makes geometry and equations much easier—and helps you avoid common mistakes with corners and intersections.
What is a Vertex?
A vertex is the point where two or more lines, rays, or edges meet. In geometry, it usually refers to the corner of a shape, such as a triangle or polygon. In algebra, it can mean the turning point of a curve like a parabola. Understanding the vertex definition is essential for topics involving angles, polygons, and graphs.
Vertex in Geometry
In geometry, a vertex is the meeting point of sides in shapes like triangles and quadrilaterals. For example, a rectangle has 4 corners, each being a vertex. The plural of vertex is vertices. Each angle in a polygon forms at a vertex. Recognising vertices helps you identify angles, label diagrams, and solve construction or proof problems. To see how vertices define polygons, check the Polygons resource, or see basic concepts at Point, Line and Plane.
Vertex in Algebra and Parabolas
In algebra, a vertex is the highest or lowest point on a parabola. This is important when working with quadratic functions. For instance, the vertex of the parabola \(y = ax^2 + bx + c\) is found with the formula below. For more on parabolas, visit Equation of Parabola.
Formula Used in Vertex Definition
To find the vertex of a parabola in the equation \(y = ax^2 + bx + c\), use:
\(
\text{Vertex } (x, y) = \left( -\frac{b}{2a}, f\left(-\frac{b}{2a}\right) \right)
\)
Here’s a helpful table to understand vertex-related vocabulary more clearly:
Vertex Terms Table
| Term | Meaning | Where Used? |
|---|---|---|
| Vertex | Corner of shape / intersection point | Geometry, Algebra |
| Vertices | Plural of vertex | All shapes |
| Vertice | Incorrect singular (avoid) | Common mistake |
| Apex | Top point, e.g., pyramid | 3D Shapes |
This table helps clarify the correct usage and avoids confusion with similar words in the vertex definition and related topics.
Worked Example – Finding Vertices in a Polygon
1. Read the question: "How many vertices does a pentagon have?"
2. Recall that a pentagon is a polygon with 5 sides.
3. Each corner where sides meet is a vertex.
4. Count the number of sides (or corners): 5.
5. So, a pentagon has 5 vertices.
Another example:
1. Find the vertex of the parabola \(y = 2(x+1)^2 - 5\).
2. This matches the standard form \(y = a(x-h)^2 + k\).
3. Compare and find \(h = -1\), \(k = -5\).
4. The vertex is at \((-1, -5)\).
Practice Problems
- Label the vertices in a quadrilateral diagram.
- Is the point (2, 3) a vertex of the shape below? Explain why or why not.
- Find the number of vertices in a regular hexagon.
- Write the vertex of the parabola \(y = -x^2 + 4x - 1\).
Common Mistakes to Avoid
- Mixing up vertex (corner point) with edges or faces of shapes.
- Thinking circles have vertices—they do not.
- Writing "vertice" as the singular form; the correct word is "vertex", plural "vertices".
- Forgetting that the vertex in algebra can be maximum or minimum, not just “top”.
Real-World Applications
Vertices appear everywhere: at street corners, the apex of a roof, and even in network graphs. Architects, engineers, and computer scientists use vertex definition to model structures, solve navigation challenges, and create digital graphics. Vedantu’s interactive resources help you practice using vertices in real contexts.
Page Summary
We explored the idea of vertex definition, how to spot vertices in shapes and graphs, and how to use the vertex formula for parabola problems. Building this foundation helps you tackle questions confidently—keep practising with Vedantu to master maths topics.
Relevant Pages: Point, Line and Plane, Polygons, Triangle and its Properties, Isosceles Triangle, Angles: Definition and Types, Equation of Parabola
FAQs on What Is a Vertex? Simple Definition, Medical Term, and More
1. What is the simple definition of a vertex?
Vertex in geometry refers to a point where two or more lines, sides, or edges meet. It is often called a corner point of a shape, such as where two sides of a triangle join.
2. What is the medical term vertex?
Vertex (medical) refers to the topmost point of the skull. In pregnancy, a baby in vertex presentation means the baby is positioned head-down in the womb, which is ideal for delivery.
3. What is the other meaning of vertex?
Besides its geometric and medical meanings, vertex can also refer to the highest or lowest point on a curve, especially in mathematics (like the vertex of a parabola), or to the point of intersection in graphs and networks.
4. What is a vertice in geometry?
Vertice is the incorrect singular of vertex. The correct plural of vertex is vertices. In geometry, vertices are the corner points of shapes like polygons or polyhedrons where edges meet.
5. What is a vertex in geometry?
In geometry, a vertex is the point where two or more edges or lines meet. For example, a triangle has three vertices and a rectangle has four vertices.
6. What is the definition of vertex in math?
In math, a vertex is a point where two or more lines, rays, or segments meet. It appears in shapes (polygons), graphs, and 3D figures.
7. What does vertex mean in algebra?
In algebra, the vertex most commonly refers to the highest or lowest point on the graph of a parabola. For a quadratic equation y = ax² + bx + c, the vertex is found at the point (-b/2a, f(-b/2a)).
8. What is the vertex of an angle?
The vertex of an angle is the point where the two sides or rays of the angle meet. For example, in angle ABC, point B is the vertex.
9. What is a vertex in a graph?
In graph theory, a vertex (plural: vertices) is a node that can be connected to other nodes by edges. Graphs are made up of vertices (points) and edges (lines connecting them).
10. What is the plural of vertex?
The plural of vertex is vertices. For example, a square has four vertices.
11. What is the vertex of a triangle?
The vertex of a triangle is any of its three corner points where two sides meet. Each triangle has three vertices.
12. What does vertex mean in pregnancy?
In pregnancy, vertex refers to the baby's head-down position before birth, called the vertex presentation. This is considered the best and safest position for normal delivery.
