Quick Links
Quick Links
SAT
SAT Prep
Good SAT Score
1600 SAT Score 1590 SAT Score 1580 SAT Score 1570 SAT Score 1560 SAT Score 1550 SAT Score 1540 SAT Score 1530 SAT Score 1520 SAT Score 1510 SAT Score 1500 SAT Score 1490 SAT Score 1480 SAT Score 1470 SAT Score 1460 SAT Score 1450 SAT Score 1440 SAT Score 1430 SAT Score 1420 SAT Score 1410 SAT Score 1400 SAT Score 1390 SAT Score 1380 SAT Score 1370 SAT Score 1360 SAT Score 1350 SAT Score 1340 SAT Score 1330 SAT Score 1320 SAT Score 1310 SAT Score 1300 SAT Score 1290 SAT Score 1280 SAT Score 1270 SAT Score 1260 SAT Score 1250 SAT Score 1240 SAT Score 1230 SAT Score 1220 SAT Score 1210 SAT Score 1200 SAT Score 1190 SAT Score 1180 SAT Score 1170 SAT Score 1110 SAT Score 1100 SAT Score 1090 SAT Score 1080 SAT Score 1070 SAT Score 1060 SAT Score 1050 SAT Score 1040 SAT Score 1030 SAT Score 1020 SAT Score 1010 SAT Score 1000 SAT Score 990 SAT Score 980 SAT Score 970 SAT Score 960 SAT Score 950 SAT Score 940 SAT Score 930 SAT Score 920 SAT Score 910 SAT Score 900 SAT Score 890 SAT Score 880 SAT Score 850 SAT Score 840 SAT Score 830 SAT Score 820 SAT Score 810 SAT Score
Acceptance Rate
Math Prep
English Prep
ACT
ACT Scores Guide
SAT Tips
ACT Tips
College Guide
Home / Mathematics / Vertices

SAT Vertices Introduction, Definition, 2D and 3D, Difference Between Vertices and Edges, Examples and FAQs

Last Updated on Mar 19, 2025
IMPORTANT LINKS
Geometry Percentage Linear Graphs Linear Equations Surface Area Logarithms Trigonometry System of Equations Complex Numbers Inequalities Complex Numbers Questions Surface Area and Volume Formulas Volume Quadratic Equation Coordinate Geometry Ratio and Proportion Linear Functions Compound Interest Hexagon Parallel Lines

What are Vertices?

A vertex is considered a special point of a mathematical object and is defined as a location where two or more straight lines or edges meet. These points, also sometimes referred to as corners, are generally denoted by uppercase letters such as A, B, C, etc.

In general, we can refer to vertices as the

  • The intersection point of two or more rays or the arms of an angle,
  • The intersection point of the adjacent edges of a polygon,
  • The intersection point of the edges of a solid figure

The most common examples of vertices are the tip of the cone, the corners of a cube or cuboid, the corners of a square, the rectangles and triangles in 2-dimensional figures, etc.

Vertices for 2d and 3d Shapes

Different geometric figures will have a different number of corners, or vertices. For example, a square has four vertices, a triangle has three, and a cone has one. So let's do a brief study on this by categorising figures into 2D and 3D.

  • 2-dimensional figures

As we already know, a 2-dimensional shape has only 2 dimensions: length and width. Some 2-dimensional figures include squares, rectangles, triangles, and circles. In 2D shapes, the vertex is defined as the point of intersection of two sides of the shape. These two sides intersect to form an angle, and thus a vertex is formed. You can have a look at the number of vertices in different 2D shapes below.

  • 3-dimensional figures 

As we know, a 3-dimensional shape has 3 dimensions: length, width, and height. Some 3-dimensional figures include cubes, cuboids, pyramids, and spheres. In 3D shapes, a "vertex" is defined as the point of intersection of two edges of the shape. In a 3-dimensional shape, multiple sides and edges can intersect from different dimensions at one point. Each intersection point forms a vertex. You can have a look at the number of vertices in different 3D shapes below,

What is the Difference Between Edges and Vertices?

The key differences between edges and vertices are as follows:

Parameters 

Edges 

Vertices 

Definition 

It is defined as the connections between the vertices.

It is defined as the points where two straight lines interest or come together to form a point.

For example: Here, we have

Edges = .

Here, we have as vertices.

Do Circles have Vertices?

No, Circles do not have Vertices. Why? This is because as per the definition, vertex is the point of intersection of straight lines and in case of circles we do not have any straight lines that intersect to form vertex. 

This doesn't mean circles do not have Edges in any sense. Circles do have an edge which forms the boundary of the shape. The length of the edge gives the circumference of the circle.

Summary

Let's the summarize entire discussion:

  • Vertex or Vertices (plural for “vertex”) are the points where two straight lines interest or come together to form a point.
  • An edge is defined as the link between the vertices or interface between two faces.

Solved Example

Example 1. List down the vertices of the given figure.

Solution 1. In the given figure, we have, as vertices.

Example 2. Mark the vertices of the given figure.

Solution 2. The vertices of the given figure can be marked as,

Example 3. Name the figures, and which have no vertices.

Solution 3. Figures with no vertices are listed as follows:

.

The concept of vertices is a basic one in geometry that is very important in 2D and 3D figures. Whether it is naming the corners of polygons or points where edges meet in solid figures, vertices are used to construct the foundation of geometric concepts. For American students gearing up for standardized tests such as the SAT, ACT, and GRE, a firm understanding of vertices can immensely upgrade problem-solving abilities and improve test scores. From identifying vertices of simple shapes to breaking down intricate figures, this understanding provides a robust foundation for cracking competitive exams. Set to upgrade your skills? Experience interactive learning and practice with the Testbook App to lead the pack in your prep journey!

What are Vertices FAQs

Vertex or Vertices (plural for “vertex”) are the points where two straight lines interest or come together to form a point.

A vertex serves as the origin of an angle.

The most common examples of vertices are the tip of the cone, the corners of a cube or cuboid, the corners of a square, the rectangles and triangles in 2-dimensional figures, etc.

Vertices are the points where two straight lines intersect or come together to form a point and an edge is defined as the link between the vertices or interface between two faces.

The shape which has 5 faces, 6 vertices and 9 edges is triangular prism.
Report An Error