This is the lesson that many teachers skip or fly through because they "assume" (in huge air quotes) that the students know what these things are before they get to high school geometry.
Unfortunately without a great understanding of points lines and planes it's almost impossible for them to grasp the tougher stuff.
Most students think that a point is something they can actually draw. They think you should be able to see it. They don't understand that it is a location and not a dot on the paper with your pencil.
1.) Points
One great way to start this lesson is to tell them to actually draw a point either on their paper or have one student draw it on the board. Them ask a different student to measure the length and with of the point with a ruler. They will do it or try to do it and give actual numbers.
Then you question them. If a point has no dimensions then how did you just give me measurements? This is where you explain that a point in geometry is a location. You can't actually draw it because the second you put your pencil on paper you can measure it.
This is a great place to transition into an explanation of what [Dimensions are]! Click here to access this lesson.
Points have no dimensions!
2.) Lines
A line has one dimension. So again you can't really draw one because when you put your pencil on the paper it has a length and a width you can measure both. The lines you actually draw in geometry class are representations of lines. We can't actually see them. Lines are used to measure distance. A great way to show this to them is have a really thin pencil and a really thick marker and tell two students to draw lines. They will visibly be able to see the thickness of the marker.
Lines are one dimensional!
3.) Planes
Planes are where things get fun. Now you are talking about space. Planes have a length and a width and are made up of infinitely many lines which are made of infinitely many points! What?
A Plane is a flat surface that has no start and no end in two of the dimensions. So can you actually draw one? Nope!
Planes are two dimensional!
Here is a video to help out! Don't make it more confusing that it already is. Your lesson on [Dimensions] will greatly reduce the confusion with these three things. The better they understand dimensions the better they will understand Points, Lines and Planes.
Here are your free worksheets and materials for this lesson!
Word Docs & PowerPoints
PDFs
Are you looking for more Geometry Lessons to incorporate in your class? Click Here to Download more Free Lesson Plans.

How to Teach Tangent Lines – Graphic Organizer

Introduction to Trigonometry

Ratios and Proportions – Bad Teacher!

Two Tips to Teach Volumes of Prisms and Cylinders

Pi Day Top 5 for Geometry Teachers

Hybrid Flipped Classroom Model

Valentine’s Day Math Activity – Classifying Quadrilaterals

Teaching Tessellations to Your Geometry Class

How to Teach Perimeter and Area of Similar Figures – in Jay Leno’s Garage

Christmas Math Worksheets

How to Create a Jeopardy Game

Polygons in the Coordinate Plane – How to use Geogebra

5 Tips for New Teachers

8 Teacher Discounts you don’t want to miss this Summer

Your Students are Cheating with this Math App

How to Setup and Use Google Classroom and Google Forms to Teach Geometry

Special Right Triangles – The Foundation of Everything Trig

How to use Google Forms and Word Clouds to Help your Students Master their Geometry Vocabulary

Interactive Geometry Teaching Techniques

The Magic Octagon – Understand congruence in terms of rigid motions

Attention Getters to Keep Your Geometry Class Locked in!

Teaching Strategies for your Inclusion Geometry Class without an Intervention Specialist

How to Teach the Properties of Quadrilaterals

Inequalities in One Triangle

Midsegments of Triangles

Classifying Polygons

Triangle Congruence by SSS and SAS

Pythagorean Theorem – NFL and Geometry

The Unit Circle – Hand Trick

How to make Geometry Interesting

How to Teach Circles Using the Common Core Standards?

Full Year of Geometry Lesson Plans

How a Rock Star Geometry Teacher Uses the iPad to Educate

Tessellation Project

Are you a Geometry Teacher with No Textbooks or Geometry Worksheets?

Geometry Games – Dance Dance Transversal

3 Ways to Make Your Life Easier as a Geometry Teacher Without More Geometry Worksheets

Parallel Lines and Transversals

Planning a Proof

Reasoning and Proof

How to Deal with a Class Clown – Classroom Management Strategies

Geometry Lessons  The Game Has Changed  Common Core Standards

Points Lines and Planes

How to Teach Dimensions – Geometry

Lesson for the First Day of Geometry Class