Designing a Winner addresses the following Common Core State Standards in High School Geometry.** **

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| 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. |

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| Use coordinates to prove simple geometric theorems algebraically. |

| 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. |