Missouri Geometry Math Standards

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G.CO Congruence

• G.CO.A Experiment with transformations in the plane.
  • G.CO.A.1 Define angle, circle, perpendicular line, parallel line, line segment and ray based on the undefined notions of point, line, distance along a line and distance around a circular arc.
  • G.CO.A.2 Represent transformations in the plane, and describe them as functions that take points in the plane as inputs and give other points as outputs.
  • G.CO.A.3 Describe the rotational symmetry and lines of symmetry of two-dimensional figures.
  • G.CO.A.4 Develop definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.
  • G.CO.A.5 Demonstrate the ability to rotate, reflect or translate a figure, and determine a possible sequence of transformations between two congruent figures.
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• G.CO.B Understand congruence in terms of rigid motions.
  • G.CO.B.6 Develop the definition of congruence in terms of rigid motions.
  • G.CO.B.7 Develop the criteria for triangle congruence from the definition of congruence in terms of rigid motions.
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• G.CO.C Prove geometric theorems.
  • G.CO.C.8 Prove theorems about lines and angles.
  • G.CO.C.9 Prove theorems about triangles.
  • G.CO.C.10 Prove theorems about polygons.
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• G.CO.D Make geometric constructions.
  • G.CO.D.11 Construct geometric figures using various tools and methods.
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G.SRT Similarity, Right Triangles, and Trigonometry

• G.SRT.A Understand similarity in terms of similarity transformations.
  • G.SRT.A.1 Construct and analyze scale changes of geometric figures.
  • G.SRT.A.2 Use the definition of similarity to decide if figures are similar and to solve problems involving similar figures.
  • G.SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
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• G.SRT.B Prove theorems involving similarity.
  • G.SRT.B.4 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
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• G.SRT.C Define trigonometric ratios, and solve problems involving right triangles.
  • G.SRT.C.5 Understand that side ratios in right triangles define the trigonometric ratios for acute angles.
  • G.SRT.C.6 Explain and use the relationship between the sine and cosine of complementary angles.
  • G.SRT.C.7 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles.
  • G.SRT.C.8 Derive the formula A = 1/2 ab sin(C) for the area of a triangle.
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G.C Circles

• G.C.A Understand and apply theorems about circles.
  • G.C.A.1 Prove that all circles are similar using similarity transformations.
  • G.C.A.2 Identify and describe relationships among inscribed angles, radii and chords of circles.
  • G.C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
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• G.C.B Find arc lengths and areas of sectors of circles.
  • G.C.B.4 Derive the formula for the length of an arc of a circle.
  • G.C.B.5 Derive the formula for the area of a sector of a circle.
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G.GPE Exploring Geometric Properties with Equations

• G.GPE.A Translate between the geometric description and the equation for a conic section.
  • G.GPE.A.1 Derive the equation of a circle.
  • G.GPE.A.2 Derive the equation of a parabola given a focus and directrix.
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• G.GPE.B Use coordinates to prove geometric theorems algebraically.
  • G.GPE.B.3 Use coordinates to prove geometric theorems algebraically.
  • G.GPE.B.4 Prove the slope criteria for parallel and perpendicular lines and use them to solve problems.
  • G.GPE.B.5 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
  • G.GPE.B.6 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
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G.GMD Geometric Measurement and Dimension

• G.GMD.A Explain volume formulas and use them to solve problems.
  • G.GMD.A.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.A.2 Use volume formulas for cylinders, pyramids, cones, spheres and composite figures to solve problems.
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• G.GMD.B Visualize relationships between two-dimensional and three-dimensional objects.
  • G.GMD.B.3 Identify the shapes of two-dimensional cross-sections of three-dimensional objects.
  • G.GMD.B.4 Identify three-dimensional objects generated by transformations of two-dimensional objects.
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G.MG Modeling with Geometry

• G.MG.A Apply geometric concepts in modeling situations.
  • G.MG.A.1 Use geometric shapes, their measures and their properties to describe objects.
  • G.MG.A.2 Apply concepts of density based on area and volume in modeling situations.
  • G.MG.A.3 Apply geometric methods to solve design mathematical modeling problems.
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G.CP Conditional Probability and Rules of Probability

• G.CP.A Understand independence and conditional probability and use them to interpret data.
  • G.CP.A.1 Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections or complements of other events.
  • G.CP.A.2 Understand the definition of independent events and use it to solve problems.
  • G.CP.A.3 Calculate conditional probabilities of events.
  • G.CP.A.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.
  • G.CP.A.5 Recognize and explain the concepts of conditional probability and independence in a context.
  • G.CP.A.6 Apply and interpret the Addition Rule for calculating probabilities.
  • G.CP.A.7 Apply and Interpret the general Multiplication Rule in a uniform probability model.
  • G.CP.A.8 Use permutations and combinations to solve problems.