How to Learn and Revise Geometry Constructions for Leaving Cert and Junior Cycle Maths

All Junior Cycle and Leaving Cert students (Higher and Ordinary level) have a set number of geometric constructions that they need to be able to do. In this article, we’re going to look at geometric constructions in general, and how to learn and practise constructions. For those in a hurry, we’re adding links to demo videos, which show you exactly how to do each of the constructions that you need. We suggest you review the rest of this article and come back to these links, we don’t want you to miss out on some great advice!

Demonstration Videos for Each Exam Level Junior Cycle (O) – Constructions 1 to 2, 4 to 6, and 8 to 15 inclusive Junior Cycle (H) – Constructions 1 to 15 inclusive Leaving Cert (O) – Constructions 1 to 2, 4 to 6, and 8 to 21 inclusive Leaving Cert (H) – Constructions 1 to 22 inclusive Don’t forget to read the advice below, to make your revision of constructions more effective.

What are geometric constructions? Geometric constructions are a method of drawing angles, lines and shapes accurately using a compass, straight-edge and pencil. You might be asked to bisect an angle using a compass and straight-edge, but without using a protractor. This can help you to gain an insight into geometry. For example, Construction 2, bisecting a line segment, is based on the geometry of isosceles triangles. We use the properties of isosceles triangles to allow us to divide a line segment into two equal parts, without using a ruler.

Drawing constructions is a hands-on skill that you can be asked to demonstrate in your Leaving Cert maths exam. You could be asked to show one construction, or a combination of more than one constructions, or a variation on some of the constructions.

How to practise constructions It’s usually best to learn the constructions in numerical order, as some of the later constructions depend on the techniques learned in earlier constructions. You could try to learn the constructions by viewing the diagrams in your textbook. However, this is really a hands-on skill and you need to actually practice doing constructions on paper to get used to using your geometry set accurately and efficiently. The best way to do this is to view our video demonstrations to see a real teacher using her geometry set to draw the actual constructions. Here are our recommended steps:

Watch the demonstration at full speed to get an overview of the method.
Then go back and play it again, while doing the actual construction yourself at the same time. You could even slow down the video playback speed, or pause the video if needed.
Close the video, take a fresh sheet of paper and test yourself, to see if you can do the construction without any help. This is the key step!
Repeat this process until you can complete the construction to a good standard in a reasonable amount of time.

Extra tips for geometric constructions Make sure you have a complete geometry set that you are familiar with, including a compass, ruler (straight-edge), protractor and set-squares. Always use a pencil for geometric constructions. Pencil is allowed by the State Exams Commission, even for exams such as maths where the exam booklet is scanned for correction. We recommend a HB pencil for drawing constructions. Make sure your pencil has a sharp point. This is important for drawing accurately. You can erase your work if you need to correct or re-draw your construction, but do not erase your construction lines e.g. if you draw arcs while constructing a triangle, leave the arc line in place to show the examiner the steps you took. Remember, ‘arcs get marks!’ If you need any further help or clarification, get in touch with us!

Those links again: Junior Cycle (O) – Constructions 1 to 2, 4 to 6, and 8 to 15 inclusive Junior Cycle (H) – Constructions 1 to 15 inclusive Leaving Cert (O) – Constructions 1 to 2, 4 to 6, and 8 to 21 inclusive Leaving Cert (H) – Constructions 1 to 22 inclusive