Geometry and Trigonometry | Leaving Cert Ordinary Maths | Alison

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Strand 2 Leaving Certificate Ordinary Level Geometry and Trigonometry - Revised

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

Free Course
This free online Leaving Certificate course teaches you Geometry and Trigonometry. It covers up to a third of Paper 2 in the Leaving Certificate Paper in the Irish curriculum. This 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. Start learning, today!





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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:

  • Recognize the different properties of shapes in mathematics
  • Define what geometric reasoning is
  • Discuss applying and using geometric reasoning to solve problems/work out solutions
  • Discus working out the equation of both parallel and perpendicular lines
  • Discuss the translation, reflection and stretching of functions
  • Discuss the general transformation of Functions
  • Calculate the equation of a circle
  • Calculate the equation of the tangent and normal 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
  • Recognize how to find a missing side or missing angle using the Sine Rule
  • Calculate areas of geometric shapes using trigonometry
  • Calculate the area of a segment of a circle


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