Junior Cert Maths Samples

_________________________________________ juniorcertsolutions.com ________________________________________ 2016 Question 6 – Higher Paper 2 Solution Given triangle abc with angles A , B , and C To prove 180 A B C ∠ + ∠ + ∠ = D Construction: Draw a line through a parallel to bc Name the angles formed X and Y Proof: X B ∠ = ∠ (alternate) Y C ∠ = ∠ (alternate) A A ∠ = ∠ ∴ A B C A X Y ∠ + ∠ + ∠ = ∠ + ∠ + ∠ but 180 A X Y ∠ + ∠ + ∠ = D a straight angle ∴ 180 A B C ∠ + ∠ + ∠ = D Comment : probably the easiest theorem they could have asked. a b c A C B Y X