Geometry is the branch of mathematics that studies the properties and relationships of shapes, angles, coordinates, and measurements. In this course, you will learn how to apply the principles and techniques of geometry to solve problems and prove theorems. You will explore topics such as:
- Transformations: how to move, rotate, reflect, and scale shapes on a plane or in space.
- Congruence: how to determine if two shapes are congruent, meaning they have the same size and shape, and how to use congruence criteria for triangles and other polygons.
- Similarity: how to determine if two shapes are similar, meaning they have the same shape but not necessarily the same size, and how to use similarity criteria and proportions to find missing lengths and angles.
- Proofs: how to write logical arguments that show why a statement is true, using definitions, postulates, theorems, and algebraic reasoning.
- Trigonometry: how to use the ratios of the sides of right triangles, known as sine, cosine, and tangent, to find missing angles and lengths, and how to apply them to real-world situations such as navigation, surveying, and astronomy.
- Analytic geometry: how to use coordinates and equations to represent and analyze geometric figures such as lines, circles, parabolas, and ellipses
- Conic sections: how to derive the equations and properties of the four types of conic sections (circles, ellipses, parabolas, and hyperbolas) from slicing a cone at different angles.
- Circle theorems: how to use theorems about angles, arcs, chords, tangents, secants, and inscribed polygons in circles to solve problems and prove statements.
- 3D shapes: how to calculate the surface area and volume of various solids such as prisms, pyramids, cylinders, cones, spheres, and hemispheres.
By the end of this course, you will have a solid foundation in geometry that will prepare you for more advanced courses in mathematics.
You will also develop your spatial reasoning skills and your ability to think creatively and critically. This course is suitable for students who have completed Algebra 1 or equivalent.
Each session will occur once a week. I have already posted the first 3 courses in this series. I will continue to add more courses as the series progresses as I see how we are moving along.
