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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 course 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. The 3 mandatory ratio theorems are: Theorem 11: If three parallel lines cut off equal segments on some transversal line, then they will cut off equal segments on any other transversal. Theorem 12: A line drawn parallel to one side of a triangle divides the other two sides in the same ratio. Theorem 13: If two triangles ABC and A’B’C’ are similar, then their sides are proportional, in order |AB|/|A'B'| =|BC|/|B'C'| =|CA|/|C'A'|