Geometry and Trigonometry | Leaving Cert Higher Level Maths | Alison

Strand 2 Leaving Certificate Higher Level Geometry and Trigonometry - Revised

This free online maths course covers up to a third of the new Paper 2 in the Leaving Certificate Paper in the Irish curriculum.

Free Course
This free online course on Geometry and Trigonometry will be a great support to any student studying maths in their Leaving Cert. And also will be a guide for anyone studying maths in this area. 'Geometry and Trigonometry' is the second of two strands which can be seen in paper 2 of the Project Maths Course in the Irish curriculum. This topic covers much of the new Leaving Certificate Paper.
  • Duration

    6-10 Hours
  • Assessment

  • Certification

  • Responsive






View course modules


Co-ordinate Geometry and Synthetic Geometry are frequently used in real life to help us understand the transformations and dimensions of shapes and figures (lines, polygons, triangles and circles). Synthetic geometry involves the examination of shapes by means of axioms and theorems. Co-ordinate geometry studies circles and lines using a fixed set of co-ordinates.

Trigonometry involves the 'real life' measurements of angles, length and circular measure in both three and two dimensions. The use of trigonometry can be seen in the areas of building and construction, quantity surveying, and in architecture generally. This strand is one of the most applicable areas of the Leaving Certificate project mathematics syllabus and it allows students to gain experience of real-world problems.

This Strand will merge the mathematical aspects of Geometry and Trigonometry with good examples of real-life application. This is a very accesable course, with interesting subject matter.

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Synthetic Geometry

Coordinate Geometry



Course assessment

Learning Outcomes

Having completed this course students will be able to:

  • Define what geometric reasoning
  • Discuss applying and using geometric reasoning to solve problems/work out solutions
  • Discuss the concepts and processes used to prove a theorem to be true
  • Discus working out the equation of both parallel and perpendicular lines
  • Discuss the translation, reflection and stretching of functions
  • Calculate the equation of a circle
  • Recognize how to find angles using the Sine, Cosine and Tangent Ratios
  • Recognize how to find sides on a triangle using the Sine, Cosine and Tangent Ratios
  • Discuss what Radians are and their uses
  • Identify how to sketch a trigonometric function on a graph
  • Recognize how to solve trigonometric equations
  • Recognize how to prove the sine and cosine rules to be true
  • Calculate areas of geometric shapes using trigonometry


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