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.
Description
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.
Start Course NowModules
Synthetic Geometry

Synthetic Geometry  Learning Outcomes

Properties of Shapes

Geometric Reasoning 1

Geometric Reasoning 2

Geometric Reasoning 3

Synthetic Geometry  Lesson Summary
Coordinate Geometry

Coordinate Geometry  Learning Outcomes

Geometry with Coordinates

Equation of a Straight Line

Parallel Lines

Perpendicular Lines

The Graphs of y=kx^n

Translation of Functions

Reflection of Functions

Stretching Functions

General Transformation of Functions

Equation of a Circle 1  Centre (0,0)

Equation of a Circle 2  (Centre Not 0,0)

Diameter of a Circle

Tangent and Normal to a Circle

Coordinate Geometry  Lesson Summary
Trigonometry

Trigonometry  Learning Outcomes

Finding Angles with Sine Ratio

Finding Sides with the Sine Ratio

Finding Angles with the Cosine Ratio

Finding Sides with the Cosine Ratio

Finding Angles with the Tangent Ratio

Finding Sides with the Tangent Ratio

Finding a Missing Side with the Sine Rule

Finding a Missing Angle with the Sine Rule

Problem Solving with the Cosine Rule

Finding Areas with Trigonometry

Area of a Segment

Trigonometry  Lesson Summary
Course assessment
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
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Certificate course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Certificate course, you have the option to acquire an official Certificate, which is a great way to share your achievement with the world. Your Alison Certificate is:
Ideal for sharing with potential employers  include it in your CV, professional social media profiles and job applications
An indication of your commitment to continuously learn, upskill and achieve high results
An incentive for you to continue empowering yourself through lifelong learning
Alison offers 3 types of Certificates for completed Certificate courses:
Digital Certificate  a downloadable Certificate in PDF format, immediately available to you when you complete your purchase
Certificate  a physical version of your officially branded and securitymarked Certificate, posted to you with FREE shipping
Framed Certificate  a physical version of your officially branded and securitymarked Certificate in a stylish frame, posted to you with FREE shipping
All Certificates are available to purchase through the Alison Shop. For more information on purchasing Alison Certificates, please visit our FAQs. If you decide not to purchase your Alison Certificate, you can still demonstrate your achievement by sharing your Learner Record or Learner Achievement Verification, both of which are accessible from your Dashboard. For more details on our Certificate pricing, please visit our Pricing Page.