Today we’re going to cover the fundamentals terms in geometry.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
We’re going to uncover the theories behind them and walk through several examples.
Let’s get started!
So what are the basic elements?
The ideas and definitions that help us to formulate and represent patterns and shapes, make predictions, and understand the properties of objects and space.
And the most basic terms necessary for success in geometry are:
- Points
- Lines
- Planes
- Segments
- Rays
Three Undefined Terms In Geometry
1. Points
Definition
A point denotes a specific location and has no dimension (i.e., width, length or depth). We describe a point using a small dot and a capital letter.
Example
Points in Geometry
2. Lines
Definition
A line is a straight path that extends indefinitely in two directions and has no thickness. And from Algebra, we know that we need two points to indicate a line, we represent a line with two arrowheads over two points on the same line or by using a cursive lowercase letter.
Example
Lines in Geometry
3. Planes
Definition
To visualize a plane, I want you to think of a piece of paper or wall that extends in all directions without end. A plane extends in two dimensions with no thickness or boundary and is represented using three points or with a capital letter typically found in the corner of the plane.
Example
Planes in Geometry
Collinear vs. Coplanar
It is important to note that for all points that lie on the same line are called collinear points, as Math Planet accurately states, and all points that lie on the same plane are called coplanar points. Moreover, while any three points are coplanar, we must select three noncollinear points when naming a plane.
Collinear Points
Coplanar Example
Line Segments and Rays
A line segment, or segment, is a part of a line and contains two endpoints and all points between them. Whereas a ray consists of one endpoint, or initial point, and extends in only one direction. When writing lines, planes, or segments, the order of each point is not important but when naming rays we must always list the endpoint first.
Line Segments in Geometry
Rays in Geometry
Together we will look at the theory behind these terms and accurately identify and represent them all while working through countless examples.
Points, Lines, & Planes – Lesson & Examples (Video)
38 min
- Introduction to points, lines and planes
- 00:00:24 – Defining terms: Point, Line, Plane, Collinear, and Coplanar
- 00:08:40 – Identify each of the following points (Examples #1-4)
- Exclusive Content for Member’s Only
- 00:15:03 – True or false given the diagram of two planes (Examples #5-10)
- 00:18:57 – True or false about collinear and coplanar theory (Examples #11-16)
- 00:21:49 – Term Definitions: Line Segments and Rays
- 00:27:33 – Name the segments or rays given the illustration (Examples #17-20)
- Practice Problems with Step-by-Step Solutions
- Chapter Tests with Video Solutions
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calcworkshop.com has been a phenomenal experience! Difficult subject matter is explained clearly and I felt I learned it better than in class.
I decided to subscribe about 12 weeks into the 16 week Calculus I class. So far it has helped tremendously. I wish I had signed up at week 1. I look forward to learning with Jenn and the Calcworkshop for future classes.Thank you, Jenn!Regards,Frank
CalcWorkshop was a wonderful resource as someone going onto a college calculus 1 class after not having taken a math course in a year! Jenn always explained things in a logical order that built upon previous lessons, and the way she explained topics was always easy to understand. Calcworkshop saved this semester for me, and I couldn't be more grateful to have found this site. :)
Anyone struggling with math at any level would greatly benefit from this product. I signed up for it immediately after getting a D on my first exam in calculus 2 and ended up getting A's and B's on the remaining exams, getting a B overall in the class. Jenn breaks down the topics, without skipping any steps, in a way that makes them very easy to understand. I highly recommend this product!
Amazing website. I've passed calculus 2 and 3. I went from barley passing to passing with an A. I didn't need to take my final exam because my grades were good enough.
Calcworkshop is an exceptionally comprehensive mathematics learning platform, spanning from basic algebra to advanced topics like Calculus III, Linear Algebra, and Differential Equations. Its standout feature is the vast number of practice problems, each accompanied by detailed, step-by-step explanations, effectively teaching learners how to approach and solve complex mathematical concepts. The instructor behind Calcworkshop is notably exceptional, delivering lessons with elegance, humility, and clarity, making even challenging topics approachable and enjoyable. Her teaching style combines rigorous mathematical proofs with intuitive analogies, creating an engaging and supportive learning atmosphere. Users consistently experience improved understanding, increased confidence, and significantly better academic performance. Calcworkshop effectively transforms mathematics from an intimidating subject into an exciting and manageable adventure. Ultimately, its unique combination of breadth, depth, engaging instruction, and personalized support makes Calcworkshop unmatched among online math learning resources
My experience was amazing. I learned so much and it really helped me through my classes.
I have been taking my college math courses online because I work full time. It was extremely hard for me to teach myself the material from the textbook without anyone explaining what needed to be done and it was trial, and error and I quickly fell behind in Calculus and Calculus 2. I discovered Calc Workshop a few weeks ago and gave it a try. I went back several courses to refresh what I've learned in the past and I already know more now than I ever did taking the course online. Jen does an amazing job of explaining the material, giving the formulas, and showing where the formulas come from so that you don't HAVE to memorize as much. She also gives helpful tips on how to memorize the rest. I have messaged to ask her several questions and she has responded before the end of the next day every time with exactly the answer I needed. I intend to use Calc Workshop throughout the rest of my college math.
Jenn thoroughly explains every move that she makes! She' s easy to understand and responds when emailed with questions! Jenn is saving my Differential Equations grade!
Calcworkshop was/is an excellent resource for anyone interested in or currently learning math. I started my Math degree at 26, spending absolutely 0 time doing math between 18 and then. I did not even know how to FOIL. The subscription got me up to speed pretty quick and then I used it for a few other courses. Couldn't recommend it enough