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Module 4: Geometry and Ratio Proof – Leaving Cert Higher Level Maths In this module, we’ll cover the following topics: - A review of basic angle facts - The three mandatory ratio proofs - Circle theorems We begin with a quick refresher on key angle facts from Junior Cert, and then shift our focus to the ratio proofs. These three theorems are mandatory for Leaving Cert Higher Level, and one of them appears on the exam almost every year. These proofs can be tricky to understand at first. When students don’t fully grasp them, memorising the steps becomes much harder. But once you do understand the reasoning behind each proof, committing them to memory becomes far easier — and much more effective. In the exam, this question is usually worth 15 marks and tends to be all or nothing. Students who have properly learned the proofs typically earn full marks. For those who haven’t, it’s hard to even get started, and many end up leaving the question blank. In this short but important module, I will clearly explain all three ratio proofs. You’ll find printable downloads with two versions of each one: An annotated version, where I explain the logic and reasoning step-by-step A formal version, laid out exactly as required by the Leaving Cert marking scheme You’ll also have access to a video explanation of each proof, including study tips to help you memorise them more easily and confidently. We won’t be required to prove the circle theorems, but we do need to understand and apply them. These will come in particularly useful later, especially when we dive into circle geometry.