Geometry

Missouri Learning Standards

Unit 1: Tools of Geometry

• 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.D.11 Construct geometric figures using various tools and methods.
• G.GPE.B.5 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Unit 2: Reasoning & Proof

• G.CO.C.8 Prove theorems about lines and angles.

Unit 3: Parallel & Perpendicular Lines

• 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.C.8 Prove theorems about lines and angles.
• G.CO.C.9 Prove theorems about triangles.
• G.CO.D.11 Construct geometric figures using various tools and methods.
• G.GPE.B.4 Prove the slope criteria for parallel and perpendicular lines and use them to solve problems.
• G.MG.A.3 Apply geometric methods to solve design mathematical modeling problems.

Unit 4: Congruent Triangles

• G.CO.C.9 Prove theorems about triangles.
• G.CO.D.11 Construct geometric figures using various tools and methods.
• G.SRT.B.4 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Unit 5: Relationships Within Triangles

• G.CO.C.8 Prove theorems about lines and angles.
• G.CO.C.9 Prove theorems about triangles.
• G.CO.D.11 Construct geometric figures using various tools and methods.
• G.SRT.B.4 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
• 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.

Unit 6: Polygons & Quadrilaterals

• G.CO.C.10 Prove theorems about polygons.
• G.CO.D.11 Construct geometric figures using various tools and methods.
• G.SRT.B.4 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
• G.GPE.B.3 Use coordinates to prove geometric theorems algebraically.
• G.GPE.B.6 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

Unit 7: Similarity

• G.CO.D.11 Construct geometric figures using various tools and methods.
• G.SRT.B.4 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
• G.SRT.C.5 Understand that side ratios in right triangles define the trigonometric ratios for acute angles.
• G.GPE.B.4 Prove the slope criteria for parallel and perpendicular lines and use them to solve problems.

Unit 8: Right Triangles & Trigonometry

• 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.MG.A.1 Use geometric shapes, their measures and their properties to describe objects.

Unit 9: Transformations

• 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.
• 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.
• 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.

Unit 10: Area

• 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.D.11 Construct geometric figures using various tools and methods.
• G.SRT.C.8 Derive the formula A = 1/2 ab sin(C) for the area of a triangle.
• 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.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.
• G.GPE.B.6 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
• 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.MG.A.1 Use geometric shapes, their measures and their properties to describe objects.

Unit 11: Surface Area & Volume

• 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.
• 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.
• 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.

Unit 12: Circles

• G.CO.D.11 Construct geometric figures using various tools and methods.
• 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.
• 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.
• 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.

Unit 13: Probability

• 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.CPA.6 Apply and interpret the Addition Rule for calculating probabilities.
• G.CPA.7 Apply and Interpret the general Multiplication Rule in a uniform probability model.
• G.CP.A.8 Use permutations and combinations to solve problems.