Geometry Basics: Parallel Lines and Congruent Triangles
This free online course describes how symbolic logic draws conclusions from statements and proving congruent triangles.Publisher: ADU
CertificationView course modules
This course is the first in a series of geometry topics in mathematics for general studies. It explains more about geometric concepts, Euclidean geometry, and congruent triangles. The free online course begins by introducing you to symbolic logic. Logical statements can be analyzed by using symbols. When we try to draw conclusions from statements, we find that their meanings and relationships to other statements are not always clear. By representing these statements using symbolic logic, we can more easily come to valid conclusions. Conditional statements make appearances everywhere. In our everyday lives, events can easily be represented by the expression “If P then Q.” Conditional statements are indeed important. You will learn about the differences between conditional and biconditional statements. A truth table is a table whose columns are statements, and whose rows are possible scenarios. The table contains every possible scenario and the truth values that would occur. This course outlines the importance of truth tables, tautologies, and equivalence relations. Formal proofs consist of a sequence of statements that are used to demonstrate the logical necessity of a given conclusion. You will learn how to prove the validity of an argument.
The course then introduces you to the study of critical thinking, which allows us to prove statements are true. Instead of making a truth table for every argument, we may be able to recognize certain common forms of arguments that are valid or invalid. If we can determine that an argument fits one of the common forms, we can immediately state whether it is valid or invalid. These laws of inference allow us to prove mathematical statements are true. In propositional logic and Boolean algebra, De Morgan's laws are a pair of transformation rules that are both valid rules of inference. The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation. You will learn about the application of this law and the different ways in which it is defined. Quantifier expressions are marks of generality. They come in a variety of categories in English, but determiners like “all”, “each”, “some”, “many”, “most”, and “few” provide some of the most common examples of quantification. This course outlines some of the most common quantifiers with the aid of examples.
Furthermore, this course introduces you to Euclidean Geometry. Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician, Euclid. In this course, you will learn about the relationships between figures in both 2-dimensional planes and 3-dimensional spaces. Although there are many types of geometries that are based on different surfaces, the planar surface best approximates the small surfaces we deal with on a daily basis. To create a geometric system, a postulate system needs to be established. Euclid, a Greek mathematician, created a set of assumptions or postulates from which he drew conclusions. These are the rules we will use in studying Euclidean Geometry. Next, you will be introduced to Congruent Triangles. In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. You will learn about the methods for proving triangles congruent and the inequalities of a triangle. So, register for this course and start your learning today.Start Course Now
Symbolic Logic - Learning Outcomes
Sentences and Statements
Truth Tables, Tautologies, and Equivalence Relations
Symbolic Logic - Lesson Summary
Symbolic Logic - Assessment
Introduction to Euclidean Geometry
Introduction to Euclidean Geometry- Learning Outcomes
Concept of Euclidean Geometry
Classification of Triangles
Parallel Lines, Angles and Polygons
Introduction to Euclidean Geometry - Lesson Summary
Introduction to Euclidean Triangle - Assessment
Congruent Triangles - Learning Outcomes
Proving Congruent Triangles
Medians, Angle Bisectors and Altitudes in a Triangle
Congruent Triangles - Lesson Summary
Congruent Triangles - Assessment
Upon the successful completion of this course, you should be able to:
- Analyze the different laws of geometry.
- Differentiate between conditional and biconditional statements.
- List the ways of defining De Morgan’s law.
- Describe the concept of euclidean geometry.
- Explain the classification of triangles.
- Analyze the postulates of equality and equivalence relations.
- Explain the criteria for the congruence of triangles.
- List the methods for proving triangles congruent.
- Differentiate between the medians, angle bisectors, and altitudes in a triangle.
- Discuss the properties of a triangle.
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