MT3500: Geometry

Course Description

Are you interested in learning how to think like a lawyer- engineer- artist- or architect? Learning Geometry will help students recognize and become aware of the many applications of geometric thinking in the world around us. This course is based on the Common Core State Standards for High School Geometry. Topics include: transformations- similarity and congruence- trigonometry and right triangle relationships-measurement- circle properties- and algebraic applications. There are opportunities to apply geometric concepts in modeling situations; such as- solving design problems. Emphasis will be placed on developing critical thinking skills as they relate to logical reasoning and argument.

Essential Standards

• Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). (CCSS.Math.Content.HSG-CO.A.2)
• Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. (CCSS.Math.Content.HSG-CO.A.5)
• Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. (CCSS.Math.Content.HSG-CO.B.6)
• Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. (CCSS.Math.Content.HSG-CO.B.8)
• Prove theorems about triangles. (CCSS.Math.Content.HSG-CO.C.10)
• Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). (CCSS.Math.Content.HSG-CO.D.12)
• Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. (CCSS.Math.Content.HSG-GMD.A.3)
• 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 ratios). (CCSS.Math.Content.HSG-MG.A.3)
• 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. (CCSS.Math.Content.HSG-SRT.A.2)
• Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. (CCSS.Math.Content.HSG-SRT.A.3)
• Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. (CCSS.Math.Content.HSG-SRT.B.5)
• Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. (CCSS.Math.Content.HSG-SRT.C.8)