This discovery learning activity will help students find the ratios between the sides in 45-45-90 triangles, by reviewing properties of an isosceles triangle. Then students discover the ratios in 30-60-90 triangles by dividing an equilateral triangle in half. Students first look at examples and generalize any patterns that they see before finding these ratios algebraically.
This is can be included as part of a unit on right triangles and Pythagorean Theorem as it builds off of these concepts. It also helps students review properties of similar triangles as well as properties of special segments in triangles.