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.

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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!

 

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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.