Strand 2 Ordinary Level Geometry and Trigonometry

Gain a better understanding of synthetic geometry, coordinate geometry, and trigonometry, with this free math course.

Free Course
Geometry and Trigonometry are part of the first phase of the new Project Maths Course. It covers up to a third of the new Paper 2 in the Leaving Certificate Paper in the Irish curriculum. This math course will teach you about synthetic geometry. In a clear and simple manner, you will be guided through the properties of shapes and learn about geometric reasoning, as well as cover coordinate geometry, trigonometry, and more.





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Synthetic geometry is also known as axiomatic or pure geometry and is the study of geometry without the use of coordinates or formulae. It studies shapes by means of axioms and theorems. This course begins by teaching you the different concepts of synthetic geometry. You will look into the different properties of shapes and learn about geometric reasoning which is the use of critical thinking, logical arguments, and spatial reasoning to solve problems and find new relationships.

Coordinate geometry is also known as analytic geometry or cartesian geometry. It is the study of geometry using a coordinate system, in contrast to synthetic geometry. This course will teach you the different concepts of coordinate geometry. You will learn its usefulness in physics and engineering, and also in aviation and space science. You will also cover trigonometry and study the relations of the sides and angles of triangles and the relevant functions of any angles.

Synthetic Geometry and Coordinate Geometry are used in real life to help us understand the dimensions and transformations of shapes and figures such as lines, triangles, polygons, and circles. Upon the completion of this course, you will have a better understanding of key geometry axioms and theorems. So, check out the course today and learn how to properly solve for the slope and equation of a line passing through two given points, find distances and angles using Sine and Cosine Rules, and more.

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Learning Outcomes

Having completed this course students will be able to:

  • Determine the slope of a line passing through two given points
  • Find the equation of a line passing through two given points
  • Find the equation of a line perpendicular to a given line and passing through a given point
  • Determine the equation of a circle having a given centre and radius
  • Find the equation of a tangent to a given circle at a specified point
  • Find distance and angle using Sine and Cosine Rules
  • Find length of an arc and area of a sector using circular measure
  • Determine the area of a triangle given the lengths of two sides and the included angle


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