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, 2018
HSG.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, 2018
HSG.CO.D13

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

October 1, 2018
HSG.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, 2018
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, 2018
HSG.GMD.A3

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*

October 1, 2018
HSG.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
HSG.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, 2018
HSG.GPE.A2

Derive the equation of a parabola given a focus and directrix.

October 1, 2018
HSG.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, 2018
HSG.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, 2018
HSG.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