Geometry - Angles, Shapes and Area | Mathematics | Alison

Geometry - Angles, Shapes and Area - Revised

This course will guide you through different areas of Geometry such as points, lines, angles, triangles, circles, transf

Free Course
This free online geometry course will teach you about geometrical concepts such as angles, shapes and area. Geometry is the area of mathematics that deals with questions of shape, size, relative position and the properties of space for objects and shapes. This course will give you an insight into the basic and advanced mathematical concepts involved in geometry, from the properties of shapes to the tangent to a circle.





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This course in Geometry is for high school and secondary school students. The course will guide you through several different areas of Geometry such as points, lines, angles, triangles, and circles, as well as transformations and area.

The course starts off with synthetic geometry giving you an overview of the different types of shapes you encounter in geometry, then moves on the helping you establish geometric reasoning, to help you understand the shapes. Along with teaching you how to prove three different theorems to be true.

In the next module you will learn about working out geometry with coordinates, beginning with the equation of a straight line, working out the equation for parallel and perpendicular lines. Then the module moves on to sketching a curve without a graph, along with the translation, reflection and stretching of functions on a graph. Next you will learn different ways of working out the equation of a circle, about the tangent and normal to a circle. The last part of this module discusses geometry involving one or more lines, such as the angle between two.

The third module teaches you about working out the trigonometry for find the missing sides and angles using Sine Ratio, Cosine Ration, and the Tangent Ratio. After the module on trigonometry the module on radians for measurements with circles starts with introducing radians, using them to find the area of a sector of a circle. Then the module moves on the graphing trigonometric functions and the unit circle.

Lastly you will learn about calculating the length, area, and volume of different objects, form 3-cuboids to parallelograms and trapeziums. Along with how to work out the area of compound shapes and the volume of compound solid shapes.

This course would be of great interest to anyone studying secondary or high school mathematics, or any one looing to further their knowledge and skills in Mathematical geometry and geometric reasoning.

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Synthetic Geometry

Coordinate Geometry



Length, Area and Volume

Course assessment

Learning Outcomes

Having completed this course students will be able to:

  • 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
  • Calculate the length, area and volume of different shapes


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