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# Geometry

Learn how to compute length, area, and volume for a wide variety of objects. Discover relationships between angles and side lengths in right triangles.

## Content

### Length, Area, and Volume

• Calculate side lengths and areas of special right triangles using geometric reasoning and the Pythagorean theorem.
• Compute volumes and surface areas of a wide variety of solids.
• Compute arc lengths and areas of sectors of circles.
• Use the coordinate plane as a tool to compute perimeters and areas of geometric objects.

### Congruence and Similarity

• Understand congruence in terms of rigid motions and use congruence criteria to reason whether two triangles are congruent.
• Understand similarity in terms of similarity transformations and use similarity criteria to reason whether two triangles are similar.

### Trigonometry

• Understand trigonometric functions as representing ratios of side lengths in right triangles.
• Reference special right triangles as a strategy to evaluate trigonometric functions of special angles.
• Apply trigonometric functions to solve for unknown sides and angles in right triangles.
1.
Geometric Transformations
12 topics
1.1. Geometric Transformations
 1.1.1. Translations of Geometric Figures 1.1.2. Rotations of Geometric Figures 1.1.3. Rotating Objects in the Coordinate Plane Using Functions 1.1.4. Reflections of Geometric Figures in the Cartesian Plane 1.1.5. Reflections of Figures Across Arbitrary Lines 1.1.6. Dilations of Geometric Figures 1.1.7. Dilations of Figures in the Coordinate Plane 1.1.8. Stretches of Geometric Figures 1.1.9. Combining Stretches of Geometric Figures 1.1.10. Combining Geometric Transformations 1.1.11. Reflective Symmetry 1.1.12. Rotational Symmetry
2.
Congruence & Similarity
15 topics
2.2. Congruence
 2.2.1. Rigid Motions and Congruence 2.2.2. The Angle-Side-Angle (ASA) Criterion for Congruent Triangles 2.2.3. The Side-Angle-Side (SAS) Criterion for Congruent Triangles 2.2.4. The Side-Side-Side (SSS) Criterion for Congruent Triangles
2.3. Similarity
 2.3.1. Similarity and Similar Polygons 2.3.2. Side Lengths and Angle Measures of Similar Polygons 2.3.3. Areas of Similar Polygons 2.3.4. Working With Areas of Similar Polygons 2.3.5. Geometric Transformations and Similarity 2.3.6. The Angle-Angle (AA) Criterion for Similar Triangles 2.3.7. The Side-Side-Side (SSS) Criterion for Similar Triangles 2.3.8. The Side-Angle-Side (SAS) Criterion for Similar Triangles 2.3.9. Combining Similarity Criteria for Triangles 2.3.10. The Midpoint Theorem 2.3.11. The Triangle Proportionality Theorem
3.
Circles
20 topics
3.4. Circles
 3.4.1. Introduction to Circles 3.4.2. Arcs, Segments, and Sectors of Circles 3.4.3. The Circumference of a Circle 3.4.4. Areas of Circles 3.4.5. Central Angles and Arcs 3.4.6. Calculating Arc Lengths of Circular Sectors Using Angles in Degrees 3.4.7. Calculating Areas of Circular Sectors Using Angles in Degrees 3.4.8. Further Calculating Areas of Sectors Using Angles in Degrees 3.4.9. Problem Solving With Circles
 3.5.1. The Inscribed Angle Theorem 3.5.2. Problem Solving Using the Inscribed Angle Theorem 3.5.3. Thales' Theorem 3.5.4. Angles in Inscribed Right Triangles 3.5.5. Inscribed Quadrilaterals 3.5.6. Tangent Lines to Circles 3.5.7. Circle Similarity
 3.6.1. Introduction to Radians 3.6.2. Calculating Arc Length Using Angles in Radians 3.6.3. Calculating Areas of Sectors Using Angles in Radians 3.6.4. Trigonometric Ratios With Radians
4.
Coordinate Geometry
10 topics
4.7. Coordinate Geometry
 4.7.1. Parallel Lines in the Coordinate Plane 4.7.2. Finding the Equation of a Parallel Line 4.7.3. Perpendicular Lines in the Coordinate Plane 4.7.4. Finding Equations of Perpendicular Lines 4.7.5. Midpoints in the Coordinate Plane 4.7.6. The Distance Formula 4.7.7. The Shortest Distance Between a Point and a Line 4.7.8. Calculating Perimeters of Shapes in the Coordinate Plane 4.7.9. Calculating Areas of Rectangles in the Coordinate Plane 4.7.10. Calculating Areas of Triangles and Quadrilaterals in the Coordinate Plane
5.
Triangles & Trigonometry
19 topics
5.8. Right Triangles
 5.8.1. The Pythagorean Theorem 5.8.2. The 45-45-90 Triangle 5.8.3. The 30-60-90 Triangle 5.8.4. The Area of a 45-45-90 Triangle 5.8.5. The Area of a 30-60-90 Triangle 5.8.6. The Area of an Equilateral Triangle 5.8.7. Diagonals of Squares
5.9. Introduction to Trigonometry
 5.9.1. Angles and Sides in Right Triangles 5.9.2. The Trigonometric Ratios 5.9.3. Calculating Trigonometric Ratios Using the Pythagorean Theorem 5.9.4. Calculating Side Lengths of Right Triangles Using Trigonometry 5.9.5. Calculating Angles in Right Triangles Using Trigonometry 5.9.6. Modeling With Trigonometry 5.9.7. The Reciprocal Trigonometric Ratios 5.9.8. Trigonometric Ratios in Similar Right Triangles 5.9.9. Trigonometric Functions of Complementary Angles 5.9.10. Special Trigonometric Ratios 5.9.11. Calculating the Area of a Right Triangle Using Trigonometry 5.9.12. Solving Multiple Right Triangles Using Trigonometry
6.
Solid Geometry
25 topics
6.10. Introduction to Solid Geometry
 6.10.1. Identifying Three-Dimensional Shapes 6.10.2. Faces, Vertices, and Edges of Polyhedrons 6.10.3. Nets of Polyhedrons 6.10.4. Finding Surface Areas Using Nets 6.10.5. The Distance Formula in Three Dimensions 6.10.6. Euler's Formula for Polyhedra 6.10.7. The Five Platonic Solids
6.11. Rectangular Solids and Pyramids
 6.11.1. Volumes of Cubes 6.11.2. Surface Areas of Cubes 6.11.3. Face Diagonals of Cubes 6.11.4. Diagonals of Cubes 6.11.5. Volumes of Rectangular Solids 6.11.6. Surface Areas of Rectangular Solids 6.11.7. Diagonals of Rectangular Solids 6.11.8. Volumes of Pyramids 6.11.9. Surface Areas of Pyramids
6.12. Non-Polyhedrons
 6.12.1. Volumes of Cylinders 6.12.2. Surface Areas of Cylinders 6.12.3. Volumes of Right Cones 6.12.4. Slant Heights of Right Cones 6.12.5. Surface Areas of Right Cones 6.12.6. Volumes of Spheres 6.12.7. Surface Areas of Spheres 6.12.8. Conical Frustums 6.12.9. Volumes of Revolution