North Dakota Geometry Math Standards

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N Number and Quantity

• N.Q Quantities
  • Reason quantitatively and use units to solve problems
    • N.Q.1.i Use units as a way to understand problems and to guide the solution of multi-step problems (e.g., unit analysis).
    • N.Q.1.ii Choose and interpret units consistently in formulas.
    • N.Q.1.iii Choose and interpret the scale and the origin in graphs and data displays.
    • N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.
    • N.Q.3 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.

A Algebra

• A.CED Creating Equations and Inequalities
  • Create equations that describe numbers or relationships
    • A.CED.4 Rearrange formulas to isolate a quantity of interest, using the same reasoning as in solving equations.

F Functions

• F.TF Trigonometric Functions
  • Extend the domain of trigonometric functions using the unit circle
    • F.TF.1 Understand that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.

G Geometry

• G.CO Congruence
  • Experiment with transformations in the plane
    • G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and plane.
    • G.CO.2.i Represent transformations in the plane.
    • G.CO.2.ii Describe transformations as functions that take points in the plane as inputs and give other points as outputs.
    • G.CO.2.iii Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
    • G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
    • G.CO.4 Develop or verify experimentally the characteristics of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
    • G.CO.5.i Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software.
    • G.CO.5.ii Specify a sequence of transformations that will carry a given figure onto another.
    • Checkpoint opportunity
  • Understand congruence in terms of rigid motions
    • G.CO.6.i Use geometric descriptions of rigid motions to predict the effect of a given rigid motion on a given figure.
    • G.CO.6.ii Use the definition of congruence in terms of rigid motions to decide if two figures are congruent.
    • G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
    • G.CO.8 Prove two triangles are congruent using the congruence theorems such as ASA, SAS, and SSS.
    • Checkpoint opportunity
  • Prove and apply geometric theorems
    • G.CO.9 Prove and apply theorems about lines and angles.
    • G.CO.10 Prove and apply theorems about triangle properties.
    • G.CO.11 Prove and apply theorems about parallelograms.
    • Checkpoint opportunity
  • Make geometric constructions
    • G.CO.12 Make basic geometric constructions with a variety of tools and methods.
    • G.CO.13 Apply basic constructions to create polygons such as equilateral triangles, squares, and regular hexagons inscribed in circles.
    • Checkpoint opportunity
• G.SRT Similarity, Right Triangles, and Trigonometry
  • Understand similarity
    • G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor.
    • G.SRT.2.i Given two figures, use transformations to decide if they are similar.
    • G.SRT.2.ii Apply the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
    • G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
    • Checkpoint opportunity
  • Prove theorems involving similarity
    • G.SRT.4 Prove similarity theorems about triangles.
    • G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
    • Checkpoint opportunity
  • Define trigonometric ratios and solve problems involving right triangles
    • G.SRT.6 Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine, and tangent of an acute angle in a right triangle.
    • G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
    • G.SRT.8 Use special right triangles (30°-60°-90° and 45°-45°-90°), trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
    • Checkpoint opportunity
  • Apply trigonometry to general triangles
    • G.SRT.10 Solve unknown sides and angles of non-right triangles using the Laws of Sines and Cosines.
• G.C Circles
  • Understand and apply theorems about circles
    • G.C.1 Understand and apply theorems about relationships with line segments and circles including radii, diameter, secants, tangents, and chords.
    • G.C.2.i Understand and apply theorems about relationships with angles formed by radii, diameter, secants, tangents, and chords.
    • G.C.2.ii Understand and apply properties of angles for a quadrilateral inscribed in a circle.
    • G.C.3 Construct the incenter and circumcenter of a triangle. Relate the incenter and circumcenter to the inscribed and circumscribed circles.
    • G.C.4 Construct a tangent line from a point outside a given circle to the circle.
    • Checkpoint opportunity
  • Find arc lengths and areas of sectors of circles
    • G.C.5 Explain and use the formulas for arc length and area of sectors of circles.
    • Checkpoint opportunity
• G.GPE Expressing Geometric Properties with Equations
  • Use coordinates to verify simple geometric theorems algebraically
    • G.GPE.4.i Use coordinates to verify simple geometric theorems algebraically.
    • G.GPE.4.ii Use coordinates to verify algebraically that a given set of points produces a particular type of triangle or quadrilateral.
    • G.GPE.5.i Develop and verify the slope criteria for parallel and perpendicular lines.
    • G.GPE.5.ii Apply the slope criteria for parallel and perpendicular lines to solve geometric problems using algebra.
    • G.GPE.6.i Use coordinates to find the midpoint or endpoint of a line segment.
    • G.GPE.6.ii Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
    • G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles, parallelograms, trapezoids and kites.
    • Checkpoint opportunity
• G.GMD Geometric Measurement and Dimension
  • Explain surface area and volume formulas and use them to solve problems
    • G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
    • G.GMD.2 Calculate the surface area for prisms, cylinders, pyramids, cones, and spheres to solve problems.
    • G.GMD.3 Know and apply volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems.
    • Checkpoint opportunity
  • Visualize relationships between two-dimensional and three-dimensional objects
    • G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
    • Checkpoint opportunity
• G.MG Modeling with Geometry
  • Apply geometric concepts in modeling situations
    • G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
    • G.MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
    • G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
    • Checkpoint opportunity

S Statistics and Probability

• S.CP Conditional Probability and the Rules of Probability
  • Understand independence and conditional probability and use them to interpret data
    • S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
    • S.CP.2.i Understand that event A is independent from event B if the probability of event A does not change in response to the occurrence of event B.
    • S.CP.2.ii Apply the formula P(AandB) = P(A) × P(B) given that event A and B are independent.
    • S.CP.3.i Understand that the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred.
    • S.CP.3.ii Apply the formula P(AgivenB) = P(AandB)/P(B) given a conditional probability situation.
    • S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. 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 everyday situations.
  • Use the rules of probability to compute probabilities of compound events in a uniform probability model
    • S.CP.6 Find the conditional probability of A given B and interpret the answer in terms of the model.
    • S.CP.7 Apply the Addition Rule, P(AorB) = P(A) + P(B) – P(AandB), and interpret the answer in terms of the model.
    • S.CP.8 Apply the general Multiplication Rule in a uniform probability model,P(AandB) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
    • S.CP.9.i Use permutations and combinations to determine the number of outcomes in terms of the model.
    • S.CP.9.ii Use permutations and combinations to compute probabilities of compound events and solve problems.
    • Checkpoint opportunity