## Geometry

Geometry will require students to explore complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. Emphasis is placed on using deductive reasoning in the analysis of topics such as parallel lines, circles, polygon congruence, similarity, area, volume, and probability. Students receiving credit for this course cannot also receive math credit for Geometry Concepts or Geometry Honors.

**Credits:** 1.0 (0.5 per semester)

**Estimated Completion Time:** 2 semester2/18-36 weeks

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### 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.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.

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