# 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 semesters/18-36 weeks

**State Course Number: **115830

Honors

Credit Acquisition

NCAA Approved

**SEMESTER 1**

**Unit 1: Foundations of Geometry**

**Missouri Learning Standards:** You will know you have achieved the learning goal when you can:

**Concept 1: Explore the Building Blocks 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.C.8 Prove theorems about lines and angles.
- G.MG.A.1 Use geometric shapes, their measures and their properties to describe objects.

**Concept 2: Explore Measurements in the Coordinate 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.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.

**Concept 3: Explore Congruence Constructions in the Coordinate Plane**

- G.CO.D.11 Construct geometric figures using various tools and methods.
- G.GPE.B.3 Use coordinates to prove geometric theorems algebraically.

**Unit 2: Geometric Transformations**

**Missouri Learning Standards:** You will know you have achieved the learning goal when you can:

**Concept 1: Explore 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.

**Concept 2: Investigate and Apply Congruence Definitions**

- 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.

**Unit 3: Intersecting Lines**

**Missouri Learning Standards:** You will know you have achieved the learning goal when you can:

**Concept 1: Explore Parallel and Perpendicular Lines**

- G.CO.A.1 Analyze and interpret graphical displays of data.
- 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.

**Concept 2: Prove Theorems about Lines and Angles**

- 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.CO.C.8 Prove theorems about lines and angles.

**Unit 4: Triangle Geometry**

**Missouri Learning Standards:** You will know you have achieved the learning goal when you can:

**Concept 1: Prove Congruence Theorems**

- G.CO.B.7 Develop the criteria for triangle congruence from the definition of congruence in terms of rigid motions.
- G.CO.C.9 Prove theorems about triangles.
- G.SRT.B.4 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
- G.CO.C.8 Prove theorems about lines and angles.
- G.CO.D.11 Construct geometric figures using various tools and methods.

**Unit 5: Similarity**

**Missouri Learning Standards:** You will know you have achieved the learning goal when you can:

**Concept 1: Explore Similarity and Dilation**

- 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.

**Concept 2: Prove Similarity Theorems**

**G.CO.C.9 Prove theorems about triangles.**- G.SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
- G.SRT.C.5 Understand that side ratios in right triangles define the trigonometric ratios for acute angles.
- G.SRT.B.4 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
- G.MG.A.3 Apply geometric methods to solve design mathematical modeling problems.

**Concept 3: Apply Similarity Theorems **

- G.SRT.A.2 Use the definition of similarity to decide if figures are similar and to solve problems involving similar figures.
- G.SRT.B.4 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

**SEMESTER 2:**

**Unit 6: Trigonometry**

**Missouri Learning Standards:** You will know you have achieved the learning goal when you can:

**Concept 1: Investigate Right Triangle 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.SRT.C.8 Derive the formula A = 1/2 ab sin(C) for the area of a triangle.

**Concept 2: Investigate Laws of Sines and Cosines**

- A1.NQ.B.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
- HSG-SRT.D.10 Prove the Laws of Sines and Cosines and use them to solve problems. NO MLS CROSSWALK
- HSG-SRT.D.11 Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). NO MLS CROSSWALK
- G.MG.A.3 Apply geometric methods to solve design mathematical modeling problems.

**Unit 7: The Geometry of Circles**

**Missouri Learning Standards:** You will know you have achieved the learning goal when you can:

**Concept 1: Investigate Circles and Parts of 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.CO.D.11 Construct geometric figures using various tools and methods. CCSS: Construct a tangent line from a point outside a given circle to the circle.

**Concept 2: Investigate and Apply Area and Circumference Formulas **

- 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.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.

**Concept 3: Investigate and Interpret Circle Equations **

- G.GPE.A.1 Derive the equation of a circle.
- G.GPE.B.3 Use coordinates to prove geometric theorems algebraically.

**Unit 8: Triangles and Circles**

**tandards:** You will know you have achieved the learning goal when you can:

**Concept 1: Investigate Concurrency in Triangles **

- G.CO.C.10 Prove theorems about triangles.
- 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 9: Quadrilaterals and Other Polygons**

**Missouri Learning Standards:** You will know you have achieved the learning goal when you can:

**Concept 1: Construct and Explore Polygons**

- G.CO.D.11 Construct geometric figures using various tools and methods. CCSS: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
- 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.

**Concept 2: Prove and Apply Theorems about Quadrilaterals**

- G.CO.C.10 Prove theorems about polygons.
- G.GPE.B.3 Use coordinates to prove geometric theorems algebraically.

**Unit 10: 3-D Figures**

**Missouri Learning Standards:** You will know you have achieved the learning goal when you can:

**Concept 1: Investigate Cross Sections and Rotations **

- 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.3 Apply geometric methods to solve design mathematical modeling problems.

**Concept 2: Develop and Apply Volume Formulas **

- 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.
- HSG-GMD.A.2 Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. NOT A MLS
- G.GMD.A.2 Use volume formulas for cylinders, pyramids, cones, spheres and composite figures to solve problems.
- 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.