Module 4: Geometry and Ratio Proofs - Leaving Cert Higher Level Maths

Module 4: Geometry and Ratio Proof - Leaving Cert Higher Level Maths In this module we cover the following topics: -Review basic angle facts -The 3 mandatory ratio proofs -Circle Theorems After a short review of the basic angle facts from Junior Cert, we will turn our attention to the ratio proofs. There are 3 ratio proofs that are mandatary for leaving cert higher level and one of them comes up in the final exam almost every year. These theorems can be difficult to understand, and when students struggle to make sense of them, it makes it incredibly difficult to memorise the steps in the proofs. In the exam, this question is usually awarded a hefty 15 MARKS, and for students it tends to be an all-or-nothing question. When students have understood and learned the proofs, they usually get full marks. If they haven't learned the proofs, it is difficult to even get started and this question is often left blank. In this short module I will clearly explain these three ratio proofs. The printable downloads contain 2 versions of each of the proofs, with the steps laid out EXACTLY as they are required by the leaving cert marking scheme; an annotated version with the steps explained so that you can understand them, and a formal version which is exactly what you need to learn for your exam. I have also included a video explanation of each theorem which includes study tips to help you memorise them. We don't need to be able to prove the circle theorems, but we do need to understand them and apply them. They will be particularly useful when we come to circle geometry.