High School: Geometry
HSG.GMD.A3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*
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.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.CO.D13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
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.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.C10
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
October 1, 2018HSG.CO.C9
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
October 1, 2018HSG.C.A2
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
October 1, 2018HSG.C.A3
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
October 1, 2018HSG.C.A4
(+) Construct a tangent line from a point outside a given circle to the circle.
October 1, 2018