High School: Geometry
HSG.SRT.C7
Explain and use the relationship between the sine and cosine of complementary angles.
October 1, 2018HSG.SRT.C8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*
October 1, 2018HSG.SRT.D9
(+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
October 1, 2018HSG.GPE.A1
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
October 1, 2018HSG.GPE.B7
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*
October 1, 2018HSG.GPE.B6
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
October 1, 2018HSG.GPE.B5
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
October 1, 2018HSG.GPE.B4
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).
October 1, 2018HSG.GPE.A3
(+) 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.
October 1, 2018HSG.GMD.B4
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
October 1, 2018