Description

Comprehensive Geometry or 9th or 10th grade students

Geometry, known as the study of shapes, is a substantial part of the first or second grade in high school. Historically, it was the first study of math on the scene, and helped us reach to other parts of math. Therefore, it is a big deal,which you should learn about! Here we start from the ground up,using a few postulates and definitions to reach to the rest of geometry. Pre-requisite: Algebra 1

Contents of the Geometry Course:

• Points, Lines, and Planes
  When we begin,we use definitions to get rigorous with these terms. But, the student also get a familiar sense with these to help later.
• Angles
  We begin this section by defining angle using lines. Then, we introduce the importance of an angle to the student.
• Parallel and Perpendicular Lines
  We use angle to see what parallel and perpendicular lines are.After that, the student learns about parallel properties with transversals. While we don’t put that much emphasis on perpendicular lines,they still are something you learn.
• Triangles
  We continue our journey when you learn about triangles. You learn about the summation of the angles with a proof.Then, you learn about the area of a triangle,the altitude,the median, and the angle bisector.After that, you learn about triangular inequalities, and learn more about triangles.
• Quadrilaterals                                                                                                                          After we learn about triangles,we learn about quadrilaterals.The different types of quadrilaterals and their qualities are what we learn in this section.
• Transformations
  In this section, the student discovers,or reviews(probably review), the 4 most common transformations:reflection,rotation,translation,and dilation. We see in depth how each one of these work and how to combine these transformations.We also cover what a rigid transformation is.
• Congruence and Similarity 
  We see that a congruent shape is a shape that went through a rigid transformation. Building on that, we see that a similar shape is a shape that went through a dilation,and maybe a rigid transformation.The student learns about what congruence and similarity implies.Most of all though, the student learns about similar and congruent triangles, and how to prove them.
• Surface Area and Volume
  Onward to the third dimension! First,we see how to define surface area and volume. The here, we study the surface area and volume of 3-D shapes and look into how to solve them for various shapes.
• Circles
  In this section ,the student learns about circles,the various properties of angles that have relations with them,secants,tangents,line segments,and arc!
• Vectors
  In this section, we take a quick look,at vectors.We learn vector addition,subtracts,and the dot product of a vector,vector scaling,applications,2D and 3D vectors(if we can get to it),and more!

Pre-requisite: Algebra 1

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