Gizmos for South Dakota - Mathematics: Geometry (Content Standards adopted 2018)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

G-CO: : Congruence

1.1: : Experiment with transformations in the plane.

G-CO.1: : State and apply precise definitions of angle, circle, perpendicular, parallel, ray, line segment, and distance based on the undefined notions of point, line, and plane.

G-CO.2: : Represent transformations in the plane. (e.g., using transparencies and/or geometry software);

G-CO.2.a: : Describe transformations as functions that take points in the plane as inputs and give other points as outputs.

G-CO.2.b: : Compare transformations that preserve distance and angle to those that do not (e.g., translation versus dilation).

G-CO.3: : Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and/or reflections that map the figure onto itself.

G-CO.4: : Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

G-CO.5: : Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure, (e.g., using graph paper, tracing paper, or geometry software). Specify a sequence of transformations that will map a given figure onto another.

1.2: : Understand congruence in terms of rigid motions.

G-CO.6: : Use geometric descriptions of rigid motions to transform figures.

G-CO.6.a: : Predict the effect of a given rigid motion on a given figure.

G-CO.6.b: : Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

G-CO.8: : Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

1.3: : Prove geometric theorems.

G-CO.9: : Prove theorems about lines and angles. Theorems must include but not limited to: vertical angles are congruent; when a transversal intersects parallel lines, alternate interior angles are congruent and same side interior angles are supplementary (using corresponding angles postulate); points on a perpendicular bisector of a line segment are equidistant from the segment's endpoints.

G-CO.11: : Prove theorems about parallelograms. Theorems must include but not limited to: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

1.4: : Make geometric constructions.

G-CO.12: : Perform geometric constructions with a compass and straightedge. including copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines/segments, constructing a line parallel to a given line through a point not on the line.

G-CO.13: : Construct an equilateral triangle, a square, and a regular hexagon.

G-SRT: : Similarity, Right Triangles and Trigonometry

2.1: : Understand similarity in terms of similarity transformations.

G-SRT.1: : Verify experimentally and apply the properties of dilations as determined by a center and a scale factor.

G-SRT.2: : Determine whether figures are similar, using the definition of similarity and using similarity transformations.

G-SRT.3: : Use the properties of similarity transformations to establish similarity theorems. Theorems must include AA, SAS, and SSS.

2.2: : Prove theorems involving similarity.

G-SRT.4: : Prove theorems about triangles involving similarity. Theorems must include but not limited to: a line parallel to one side of a triangle divides the other two proportionally, and its converse; the Pythagorean Theorem proved using triangle similarity.

G-SRT.5: : Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

2.3: : Define trigonometric ratios and solve problems involving right triangles.

G-SRT.6: : Define, using similarity, that side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios (sine, cosine, and tangent) for acute angles.

G-SRT.8: : Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

G-C: : Circles

3.1: : Understand and apply theorems about circles.

G-C.2: : Identify and describe relationships among central angles, inscribed angles, circumscribed angles, radii, and chords.

G-C.3: : Construct, using a compass and straight edge, the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

3.2: : Find arc lengths and areas of sectors of circles.

G-C.5: : Derive using similarity the length of the arc intercepted by an angle is proportional to the radius.

G-C.5.a: : Define the radian measure of the angle as the constant of proportionality;

G-C.5.b: : Derive and apply the formula for the area of a sector.

G-GPE: : Expressing Geometric Properties with Equations

4.1: : Translate between the geometric description and the equation for a conic section.

G-GPE.1: : 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.

4.2: : Use coordinates to prove simple geometric theorems algebraically.

G-GPE.5: : Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

G-GMD: : Geometric Measurement and Dimension

5.1: : Explain volume and surface area formulas and use them to solve problems.

G-GMD.1: : Give an informal argument for the formulas for the volume of a cylinder, pyramid, sphere, and cone. Use dissection arguments, and informal limit arguments.

G-GMD.2: : Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.

G-GMD.3: : Know and apply volume and surface area formulas for cylinders, pyramids, cones, and spheres for composite figures to solve problems.

S-CP: : Statistics and Probability-Conditions Probability and Rules of Probability

7.1: : Understand independence and conditional probability and use them to interpret data.

S-CP.1: : Describe events as subsets of a sample space or as unions, intersections, or complements of other events.

S-CP.2: : Determine whether two events A and B are independent.

S-CP.3: : Determine conditional probabilities and interpret independence by analyzing conditional probability.

S-CP.4: : Construct and interpret two-way frequency tables of data. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

S-CP.5: : Recognize and explain the concepts of conditional probability and independence in everyday language and situations.

S-CP.6: : Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the result.

S-CP.8: : Apply the general Multiplication Rule, P(A and B), and interpret the result.

Correlation last revised: 9/16/2020

South Dakota - Mathematics: Geometry

Content Standards | Adopted: 2018