# Leaving Cert Higher Maths Constructions

The **Leaving Cert Higher maths **course contains 22 geometry constructions, 15 of which you will have already covered in Junior Cert Higher constructions.

Some of these first 15 form the basic steps of the more advanced constructions, so it is important to master these first. When you are comfortable with constructions 1 to 15, you can move on to the remaining 7 constructions which are required for the Leaving Cert Higher maths course.

Geometry constructions have been examined intermittently in the Leaving Cert Higher exam, and certainly not every year. However, if you are aiming for a high grade, you can’t afford to neglect this part of the course.

For general guidance on how to learn and revise maths constructions, click **here**.

Here’s the full list of Leaving Cert Higher maths constructions, and the demo videos are embedded below this.

Construction 1 – Bisector of an angle, using only compass and straight edge

Construction 2 – Perpendicular bisector of a segment, using only compass and straight edge

Construction 3 – Line perpendicular to a given line l, passing through a given point not on l

Construction 4 – Line perpendicular to a given line l, passing through a given point on l

Construction 5 – Line parallel to given line, through a given point

Construction 6 – Division of a line segment into 2, or 3 equal segments without measuring it

Construction 7 – Division of a line segment into any number of equal segments without measuring it

Construction 8 – Line segment of a given length on a given ray

Construction 9 – Angle of a given number of degrees with a given ray as one arm

Construction 10 – Triangle, given lengths of 3 sides

Construction 11 – Triangle, given SAS data

Construction 12 – Triangle, given ASA data

Construction 13 – Right-angled triangle, given length of hypotenuse and one other side

Construction 14 – Right-angled triangle, given one side and one of the acute angles

Construction 15 – Rectangle given side lengths

Construction 16 – Circumcentre and circumcircle of a given triangle, using only straight edge and compass

Construction 17 – Incentre and incircle of a triangle of a given triangle, using only straight edge and compass

Construction 18 – Angle of 60⁰ without using a protractor or set square

Construction 19 – Tangent to a given circle at a given point on it

Construction 20 – Parallelogram, given the length of the sides and the measure of the angles

Construction 21 – Centroid of a triangle

Construction 22 – Orthocentre of a triangle

**See below for our demonstration videos showing you exactly how to do these LCH maths constructions.**

If you need any further help or clarification, **get in touch** with us at any time!

#### All 22 Leaving Cert Higher Maths Constructions

**Full Playlist** – all 22 constructions on our YouTube channel

**Construction** **1** – Bisector of an angle, using only compass and straight edge

**Construction** **2** – Perpendicular bisector of a segment, using only compass and straight edge

**Construction** **3 **– Line perpendicular to a given line l, passing through a given point not on l.

**Construction 4 **– Line perpendicular to a given line l, passing through a given point on l

**Construction** **5 **– Line parallel to given line, through a given point

**Construction** **6** and **7 **– Division of a line into 2, 3 or any number of equal segments without measuring it

**Construction** **8 **– Line segment of a given length on a given ray

**Construction** **9** – Angle of a given number of degrees with a given ray as one arm

**Construction** **10** – Triangle, given lengths of 3 sides

**Construction** **11** – Triangle, given SAS data

**Construction** **12** – Triangle, given ASA data

**Construction** **13** – Right-angled triangle, given length of hypotenuse and one other side

**Construction** **14** – Right-angled triangle, given one side and one of the acute angles

**Construction** **15** – Rectangle given side lengths

**Construction 16** – To construct the circumcentre and circumcircle of a given triangle.

**Construction 17** – To construct the in-centre and in-circle of a given triangle.

**Construction 18** – Use this interactive file to construct an angle of 60 degrees.

**Construction 19** – Use this file to learn to construct the tangent to a circle at a given point on it.

**Construction 20** – Use this file to learn to construct a parallelogram, given the length of sides and the measure of the angles.

**Construction 21** – Use this file to learn to construct the centroid of a triangle.

**Construction 22 **– Use this file to learn to construct the orthocentre of a triangle.