Answer:They are especially useful when you learn about trigonometry. They are the special triangles: One has angles 30–60–90 and side lengths 1–2–sqrt3. The other has angles 45–45–90 with side lengths 1–1-sqrt2. They are important because those angles and their multiples have exact trig ratios. In Ontario they become especially relevant in grade 10 and up: any trig problem that tells you to leave your answer exact likely involves these angles and their multiples. The teacher will be looking for the studen to perform operations with fractions involving roots and simplifying without resorting to decimals (although lots of calculators can report roots in fractions now). Also, tracing the inside of each of the triangles is quick and easy to ensure that a diagram is accurate for these commonly used angles - no protractor required.