Common Core: MATH.CONTENT
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, 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.GPE.B7
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*
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.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, 2018HSF.TF.C9
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
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, 2018