- 1. Basics of Geometry
This chapter introduces students to the basic principles of geometry, including points, lines, planes, and angles.
- 2. Reasoning and Proof
This chapter introduces students to the concept of reasoning in a geometric setting, with emphasis on proving theorems about angle pairs and segments.
- 3. Parallel and Perpendicular Lines
This chapter covers parallel and perpendicular lines and planes. Also considered are angle relationships and the equations of lines and slopes.
- 4. Triangles and Congruence
This chapter explores triangles in geometry with respect to congruency and angles. Also covered are some unique types of triangles.
- 5. Relationships with Triangles
This chapter continues to explore triangles with an emphasis on triangle relationships, properties of segments and angles, and the properties associated with the sides of triangles.
- 6. Polygons and Quadrilaterals
This chapter introduces students to polygons and quadrilaterals, including parallelograms, rhombi, rectangles, squares, kites, and trapezoids.
- 7. Similarity
This chapter starts with a review of ratios and proportions and then introduces the concept of similarity. Similarity is applied to polygons, quadrilaterals, triangles, proportionality with parallel lines, dilations and fractals.
- 8. Right Triangle Trigonometry
In this chapter, the Pythagorean Theorem and its converse are proved. Then, trigonometry is introduced, starting with the tangent, sine and cosine ratios, and then extended to any triangle, through the Law of Sines and the Law of Cosines.
- 9. Circles
This chapter covers all the parts of a circle and explores the properties of tangent lines, arcs, inscribed angles, chords, angles and segments that are formed by chords, tangents and secants, equations and graphs of circles.
- 10. Perimeter and Area
In this chapter, students learn how to find the perimeter and area of triangles, quadrilaterals, polygons, and circles.
- 11. Surface Area and Volume
This chapter extends what we know about two-dimensional figures to three-dimensional shapes. Different types of 3D shapes and their parts are defined. Then, surface area and volume of prisms, cylinders, pyramids, cones, and spheres are found.
- 12. Rigid Transformations
The final chapter of Geometry transforms a figure by moving, flipping, or rotating it. First, it looks at symmetry, followed by the different transformations.