Geometry Basics, Geometric Constructions

This free online course provides a rigorous mathematical foundation for both practical and theoretical geometric thinking. The course begins by considering basic figures such as points, lines and planes. You will be introduced to the concept of parallelism and perpendicularity as well as more complicated geometric figures such as polygons. Emphasis is placed on developing critical thinking skills as they relate to logical reasoning.

What You Will Learn In This Free Course

Symbolic Logic (Part 1)

In this module, you will be introduced to symbolic logic and how you can represent statements using symbolic logic, learn about the definition of a mathematical sentence, the two types of mathematical sentences. Also, learn about compound statements and how they are formed, Conjunctions and Disjunctions with some examples.

Symbolic Logic (Part 2)

In this module, you will be introduced to Symbolic Logic (Part 2) and learn how the laws of inference allow us to prove mathematical statements are true. Learn about the rule of inference, Law of Syllogism and Disjunctive Inference. Learn how to compare the Law of Modus Tollens using the truth table with examples, DeMorgan’s law and quantifiers.

Introduction to Euclidean Geometry

In this module, you will be introduced to Euclidean Geometry, learn about the three different elements that make up all geometric planar or three-dimensional objects. Also, learn about Lines, Segments and Rays. Additionally, learn the Classification of Triangles and also postulates.

Reasoning

In this module, you will be introduced to reasoning, the definition and the two types of reasoning. Learn about how proofs can be written informally in paragraph form or how they can be set up in a 2-column T-bar format and lastlt, how you logically combine rules, laws, postulates, and theorems to obtain the desired conclusion.

Geometry Basics, Geometric Constructions and Logic – First Graded Assessment

In this module, you will review your learning so you can determine your knowledge and understanding of the following area: Symbolic Logic Introduction to Euclidean Geometry Reasoning Remember, if you do not achieve the required standard after the first attempt, you can re-take the assessment until a successful outcome is achieved.

Parallel Lines, Angles and Polygons

In this module, you will be introduced to Parallel Lines, Angles and Polygons. Learn about a triangle and how each has three exterior angles, formed by extending the sides of the triangle. Lastly, learn how to find the sum of the measures of the interior angles of a quadrilateral and how to add the angle measures of two triangles.

Trigonometry of Right Triangle

In this module, you will be introduced to Trigonometry of Right Triangle. Also, learn what the side opposite the right angle is called. Learn about the sine, cosine, and tangent of an angle with examples. Lastly, you will learn about what solving triangles using trigonometric ratios means and what the three types of trigonometric ratios are with examples.

Constructions (Part 1)

In this module, you will be introduced to Constructions and be taken through how to construct a line segment congruent to a given line segment using a compass and straight edge. Also, learn about the definition of a segment bisector and a perpendicular bisector. Additionally, learn about the median of a triangle, the three medians of a triangle and detailed information about the construction of a median to the side of a triangle. Lastly, learn how to use the converse of the Alternate Interior.

Constructions (Part 2)

In this module, you will learn about the definition of an Angle Bisector and be taken through how to construct the bisector of a given angle. Learn about how to construct a line perpendicular, understand Heron’s formula and how to find the altitude of a triangle given the sides. Lastly, be taken through detailed information about the construction of any similar triangle to a given triangle.

Constructions (Part 3)

In this module, you will learn about how to explain the construction of an equilateral triangle and learn to construct an equilateral triangle. Learn how to identify the process of locating the circumcenter of a triangle. Lastly, learn Centroid, Orthocenter and Tangents of a Triangle.

Course assessment