Common Core: MATH.CONTENT
HSG.GMD.A2
(+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
October 1, 2018HSG.GMD.A3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*
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, 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.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.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.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.B6
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
October 1, 2018HSG.CO.B8
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
October 1, 2018HSF.TF.C8
Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
October 1, 2018HSF.TF.C9
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
October 1, 2018