Common Core State
HSG.CO.C11
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
October 1, 2018HSG.CO.D12
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line … Read More “HSG.CO.D12”
October 1, 2018HSG.CO.D13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
October 1, 2018HSG.GMD.A1
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
October 1, 2018HSG.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.CO.A5
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.
October 1, 2018HSG.CO.B6
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.
October 1, 2018