The undefined terms of geometry

The Undefined Terms of Geometry

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The undefined terms of geometry serve as the building blocks for defining other terms. There are three such undefined terms, including point, line, and plane. However, even if we don’t formally define them, we can, of course, describe these terms.

There are plenty of ways in which teachers can make teaching the undefined terms of geometry exciting, and today we bring you a few awesome tips to achieve this! Use these tips in your classroom and you’ll be sure to blend learning with fun!

Tips to Teach the Undefined Terms of Geometry

Undefined Terms Of Geometry

You can explain to students that the undefined terms of geometry are words or terms that don’t require any further explanation or elaborate description. Nonetheless, it’s good to provide a brief overview of them or a brief description to make sure that children understand them.

Point

You may want to start by providing a brief description of each undefined term. Ask students to imagine a starry sky. Explain to students that a point is just like a star in the starry sky – it’s a dot indicating a location in space.

This dot can be tiny or large, but this doesn’t make any difference, as the point simply represents a location or position. So make sure to point out that a point has no size, length, width, or height. In the coordinate plane, we name points by ordered pairs (x, y).

Present a few examples of points by drawing a line on the whiteboard and placing a few points on it. Point out that we name the point with a capital letter. Then, ask the students to identify how many points there are on the line.

Line

Ask students to think of that night sky full of stars again. Then, point out that a line is a straight path through the stars that extends in opposite directions with no end. So a line goes on forever in both directions and thus has infinite length and zero width and height.

Explain that a line doesn’t have endpoints and we draw it with arrowheads on both ends. The two-sided arrow is the symbol we use for lines. Lines are named by 2 points with a 2-sided arrow above the named points

Draw a line on the whiteboard with a few points on it and ask students to identify the names for the line.

Plane

Explain to students that a plane forms a flat surface that extends without end. A plane has two dimensions – length and width, and as it extends indefinitely, it has infinite length, width, and zero height, as well as infinite lines and points.

Point out that planes are named by an uppercase script letter (for example plane m) or 3 non-collinear points on the plane. Add that non-collinear points on the plane are points that are not on the same line.

Explain that we draw a plane like a figure with four sides that looks like a parallelogram. Draw such a figure on the whiteboard to illustrate what a plane looks like. But make sure to point out that a plane has no boundaries, even though this diagram on the whiteboard has edges.

Line Segment

Describe a line segment as a part of a line between 2 endpoints. In other words, unlike lines, a line segment does not extend indefinitely in any direction and has a starting point and an endpoint.

Add that a line segment is named by its endpoints with a line without arrows above the names of the two endpoints. Draw a few line segments on the whiteboard and ask students to label and name them.

Ray

Finally, explain to students that a ray is a part of a line that consists of one endpoint and all the points on one side of the endpoint. A ray is named by its endpoint and another point on the ray.

Draw a few examples of rays on the whiteboard and ask students to identify and name them.

Additional Resources

If you have the technical means in your classroom, you can enrich your lesson with multimedia materials, such as videos. Videos will also come in handy for the visual representation of points, lines, and planes.

For instance, you can use this fun video that provides brief descriptions of the three undefined terms in geometry, followed by illustrative and colorful examples, such as dots on the tips of pencils or in the corners of boxes.

Activities to Practice the Undefined Terms of Geometry

Online Activity

This is a simple online activity by Khan Academy that will help students practice their skills at identifying and differentiating between the different undefined terms of geometry, as well as related terms. Introduce this activity at the end of your lesson.

Make sure there is a technical device for each student. Explain to students that they will do an online activity where they will have to answer several math challenges related to the undefined terms of geometry. They need to select the correct answer in the multiple-choice questions.

If a student gets stuck, they can also decide to use a hint or watch an explanatory video. In the end, provide some time for discussion and reflection. The activity is done individually, which makes it ideal for homeschooling parents as well.

Group Work

This activity will allow students to reinforce their knowledge of points, lines, planes, as well as rays, line segments, and their skills at drawing these. To implement this activity in your classroom, the only thing you will need is to print out our free Assignment Worksheet.

Divide students into groups of 3 or 4 and hand out the worksheet. Make sure there is one copy per student. Explain to students that they need to work together with the members of their group to draw, name, and label the figures and terms in the assignment.

Provide around 15 minutes for groups to complete the worksheets. After this, open a class discussion and allow space for each group to share their work and the challenges they encountered while completing the tasks.

Before You Leave…

If you enjoyed these tips and resources, we have a whole lesson on teaching the undefined terms of geometry to 4th graders! So make sure to check out our worksheets and resources on teaching this. These are all pdf files, so you’ll be able to print them out easily:

To get the Editable versions of these files, join us in the Math Teacher Coach community!

This article is based on:

Unit 7 – Geometry

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