Common Core: MATH.CONTENT
HSG.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, 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.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.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, 2018HSG.C.B5
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
October 1, 2018