Geometry (South Dakota Content Standards)

Geometry (G)

• GEO.G.CO.1 State and use exact definitions of angle, circle, perpendicular, parallel, ray, segment and distance from point, line and plane.
• GEO.G.CO.2 Represent plane transformations, e.g. with transparencies or software.
  • GEO.G.CO.2a Describe transformations as functions from points to points.
  • GEO.G.CO.2b Compare transformations that keep distance and angle with those that do not.
• GEO.G.CO.3 Describe rotations and reflections that carry a rectangle, parallelogram, trapezoid or regular polygon onto itself.
• GEO.G.CO.4 Define rotations, reflections and translations using angles, circles, perpendicular and parallel lines and segments.
• GEO.G.CO.5 Draw the image of a figure under a rigid transformation and give a sequence mapping one figure to another.
• GEO.G.CO.6 Use descriptions of rigid motions to transform figures.
  • GEO.G.CO.6a Predict what a given rigid motion does to a figure.
  • GEO.G.CO.6b Decide whether two figures are congruent using rigid motions.
• GEO.G.CO.7 Use rigid motions to show triangles are congruent exactly when matching sides and angles are congruent.
• GEO.G.CO.8 Explain how ASA, SAS and SSS follow from congruence by rigid motions.
• GEO.G.CO.9 Prove theorems about lines and angles, such as vertical angles and angles formed by a transversal of parallel lines.
• GEO.G.CO.10 Prove theorems about triangles, such as angle sum, isosceles base angles and midsegments.
• GEO.G.CO.11 Prove theorems about parallelograms, such as opposite sides and angles and bisecting diagonals.
• GEO.G.CO.12 Do compass-and-straightedge constructions: copying and bisecting segments and angles, perpendiculars and parallels.
• GEO.G.CO.13 Construct an equilateral triangle, square and regular hexagon.
• GEO.G.SRT.1 Check by experiment and use the properties of dilations with a center and scale factor.
• GEO.G.SRT.2 Decide whether figures are similar using the definition and similarity transformations.
• GEO.G.SRT.3 Use similarity transformations to establish the AA, SAS and SSS similarity theorems.
• GEO.G.SRT.4 Prove triangle theorems involving similarity, such as the side-splitter theorem and the Pythagorean Theorem.
• GEO.G.SRT.5 Use triangle congruence and similarity criteria to solve problems and prove relationships.
• GEO.G.SRT.6 Use similarity to see side ratios in right triangles as angle properties, defining sine, cosine and tangent.
• GEO.G.SRT.7 Explain and use how the sine and cosine of complementary angles relate.
• GEO.G.SRT.8 Solve right triangles in applied problems with trig ratios and the Pythagorean Theorem (modeling).
• GEO.G.C.1 Prove that all circles are similar.
• GEO.G.C.2 Describe relationships among central, inscribed and circumscribed angles, radii and chords.
• GEO.G.C.3 Construct a triangle's inscribed and circumscribed circles and prove angle facts for quadrilaterals in circles.
• GEO.G.C.4 Construct a tangent to a circle from a point outside it (plus standard).
• GEO.G.C.5 Use similarity to show arc length is proportional to the radius.
  • GEO.G.C.5a Define radian measure as the constant of proportionality.
  • GEO.G.C.5b Derive and use the sector area formula.
• GEO.G.GPE.1 Derive a circle's equation from center and radius and complete the square to find them from an equation.
• GEO.G.GPE.4 Prove geometric relationships with coordinates, e.g. whether four points form a rectangle.
• GEO.G.GPE.5 Define and use slope tests for parallel and perpendicular lines, e.g. to write the equation of such a line.
• GEO.G.GPE.6 Find the point that splits a directed segment in a given ratio.
• GEO.G.GPE.7 Use coordinates and the distance formula for polygon perimeters and for areas of triangles and rectangles (modeling).
• GEO.G.GMD.1 Argue informally for volume formulas of cylinders, pyramids, spheres and cones using dissection and limits.
• GEO.G.GMD.2 Use Cavalieri's principle in an informal argument for sphere and other solid volumes (plus standard).
• GEO.G.GMD.3 Find volume and surface area of cylinders, pyramids, cones, spheres and combined solids with formulas to solve problems (modeling).
• GEO.G.GMD.4 Identify 2D cross-sections of 3D objects and 3D solids made by rotating 2D shapes.
• GEO.G.MG.1 Describe real objects with geometric shapes and their measures, e.g. a tree trunk as a cylinder (modeling).
• GEO.G.MG.2 Use area- and volume-based density in modeling, e.g. people per square mile (modeling).
• GEO.G.MG.3 Solve design problems with geometry, e.g. meeting physical limits or keeping costs low (modeling).

Statistics and Probability (S)

• GEO.S.CP.1 Describe events as pieces of a sample space, or build them with union, intersection and complement.
• GEO.S.CP.2 Decide whether two events are independent.
• GEO.S.CP.3 Find conditional probabilities and interpret independence through them.
• GEO.S.CP.4 Build and read two-way frequency tables and use them to judge independence and estimate conditional probabilities.
• GEO.S.CP.5 Explain conditional probability and independence in plain words and daily situations.
• GEO.S.CP.6 Find P(A given B) as the share of B's outcomes also in A and interpret it.
• GEO.S.CP.7 Apply the addition rule to find the chance of A or B and explain it.
• GEO.S.CP.8 Apply the general multiplication rule to find the chance of A and B and explain it.