The What’s Your Angle, Pythagoras? Project addresses the followingin High School Geometry.
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Prove the Pythagorean identity sin2(?) + cos2(?) = 1 and use it to find sin (?), cos (?), or tan (?), given sin (?), cos (?), or tan (?), and the quadrant of the angle.
Use geometric shapes, their measures, and their properties to describe objects (e.g. modeling a tree trunk or a human torso as a cylinder.
Explain and use the relationship between the sine and cosine of complementary angles.