Geometry Worksheets

Practice and master geometry concepts with helpful walkthroughs from our elite math educators, then try practice math problems to sharpen your skills.

Vertex

By Ellen Rattin

The vertex is the point where two rays that form an angle meet, or where two sides of a polygon meet. It can be thought of as the “elbow” or the point at which an angle bends.

Why is this concept useful?

Angles are a foundational topic in geometry; much of middle school and high school geometry consists of exploring properties of figures formed by angles. Therefore, correctly understanding angles, their vocabulary and naming, is essential to accessing geometric content.

Where does this concept fit into the curriculum?

Grades 6-8, HS Geometry

How can we use the concept:

Since the vertex is a point, it is named as all points are, with a single capital letter. For example, consider the following angle:

Point B would be the vertex. The name of this angle is ∠ABC. Angles are generally named with three letters, where the middle letter is the vertex and the two other letters are points that the rays, which form the angle, pass through.

A vertex is also a point where the sides of a polygon meet. The plural of vertex is vertices. Consider the following polygon:

This hexagon has 6 vertices - points A, B, C, D, E, and F.

Sample Math Problems

1. Identify the vertex of the angle.

Solution: The vertex is at T because this is the point at which the two rays meet.


2. Kristal is asked to draw ∠CAT. Which of the following is a correct drawing of this angle?

Solution: The correct answer is A and C. We know the vertex of the angle should be A, because ∠CAT places A in the middle of the letters, indicating it is the vertex. Both answer choices A and C correctly place the vertex at A, allowing the rays to pass through points C and T. Answer B is not correct because it places the vertex at C.


3. Name all the angles with a vertex at F.

Solution: There are 3 angles with a vertex at F: ∠GFH, ∠HFJ, and ∠GFJ. All other angles in the diagram have a vertex at G, H, or J.

4. How many vertices does the following figure have?

Solution: The figure has 7 vertices - seven points at which the sides of the polygon meet.

Download FREE Math Resources

Take advantage of our free downloadable resources and study materials for at-home learning.

8 Math Hacks and Tricks to Turn Your ‘Okay’ Math Student Into a Math Champion!

One thing we teach our students at Thinkster is that there are multiple ways to solve a math problem. This helps our students learn to think flexibly and non-linearly.

Get PDF

How to Make Sure Your Child is Highly Successful and Becomes a Millionaire

As a parent, you hope your child is extremely successful and likely become the next Gates, Zuckerberg, or Meg Whitman. To set your child on the right path, there are many skills and traits that you can start building and nurturing now. Doing so plants the seeds for future success.

Get PDF

Practice Math Problems

1. Identify the vertex of the angle.

2. Draw ∠BAT. Which point is the vertex?

3. Name all the angles whose vertex is M.

4. How many vertices does the following figure have?

Related Topics

By Puja Varude

Normal Distribution

By Patricia Martin

Tossing a Coin

By Mandi Elam

Properties of Exponents

By Debi DalPezzo

Solve for x

Math Tutoring to Boost Your Child’s Math Skills & Scores by 90% in Just 3 Months – Guaranteed!

Does your child struggle with math homework or understanding tricky math concepts? Do they do okay in math, but express excitement to learn new material or advanced math?

A Thinkster Math tutor provides one-to-one support to help elementary, middle school, and high school students build confidence and master math subjects like K-8 math, pre-algebra, algebra, geometry, calculus, and more.

Our expert math tutors customize math lessons to your child’s unique needs, making learning math fun and effective. We help students improve grades, develop strong critical thinking skills through solving word problems, excel in standardized tests, and develop strong problem-solving skills.

Our expert math tutors are ready to help make your child a champion and develop strong math mastery! Sign up for our 7-day free trial and get the best math tutor for your child today!

Start 7-Day Free Trial