HSG-CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
HSG-CO.A.2: Represent transformations in the plane, 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.
HSG-CO.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
HSG-CO.C.9: Prove theorems about lines and angles.
HSG-CO.C.10: Prove theorems about triangles.
HSG-CO.D.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc).
HSG-GPE.A.2: Derive the equation of a parabola given a focus and directrix.
HSG-GPE.A.3: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
HSG-GPE.B.4: Use coordinates to prove simple geometric theorems algebraically.
HSG-GPE.B.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
HSG-GPE.B.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
HSG-GPE.B.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
HS.TT.1.1: Use appropriate technology tools and other resources to access information.
Students will learn about points, lines, and segments in order to infer about angles.
Students will learn about angles in order to infer about triangles.
Students will learn about triangles in order to infer about formulas.
Given the basic definitions of points, lines, planes, and angles, students will derive the Pythagorean Theorem.
Given the graphical display of lines, students will derive the distance formula.
Given the definitions and theorems, students will create a game to show their understanding of the material in the unit.
Students will work to find a set formula for finding the hypotenuse or missing sides of a triangle in several class examples using the information previously learned about triangles.
Working with fellow classmates, students will find the distance formula using what they have learned about the Pythagorean Theorem and graphical displays provided by the teacher.
Students will create a game as a form of review for the unit test. Working in pairs, they will choose a topic from within the unit to create a detailed game. Before the test, the students will play each other's games as review.