Designing a Winner addresses the followingin High School Geometry.
Use geometric shapes, their measures, and their properties to describe objects (e.g. modeling a tree trunk or a human torso as a cylinder.
Apply concepts of density based on area and volume in modeling situations (e.g. persons per square mile, BTU’s per cubic foot).
Apply geometric methods to solve design problems (e.g. designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on rations).
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Explain and use the relationship between the sine and cosine of complementary angles.
Use trigonometric ratios and the Pythagorean theorem to solve right triangles in applied problems.
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, ?3) lies on the circle centered at the origin and containing the point (0, 2).
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.