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Geometry

Geometry demands the mastery of topics such as Deductive Reasoning and the Laws of Logic to make mathematical arguments. Our course is designed to establish many levels of proficiency. Using the information found in our Deductive Reasoning and the Laws of Logic topic, you will aplly the Language of Geometry to make various Types of Proofs to verify relationships between angles and lines in geometric figures. Geometric proofs explain relationships between angles and shapes in Geometry. When Proving Angles are Complementary with Perpendicular Lines, step-by-step explanations and factual evidence is required. There are a variety of Methods of Proofs used in Geometry. For example, covered in our topic Testing a Generalization and Counterexamples, you will develop the skills to prove a certain relationship is not always true. By applying many different aspects of Geometry to to our Reasoning and Proofs topic, you will develop high level proficiencies required for advanced level Geometry.

- Language of Geometry
- Language of Geometry2
- Inductive Reasoning
- Conjectures
- Counterexamples
- Deductive Reasoning and the Laws of Logic
- Using Deductive Logic
- Law of Detachment
- Law of Syllogism
- Converse of an If-Then statement
- Inverse of an If-Then Statement
- Contrapositive of an If-Then Statement
- Converse, Inverse, and Contrapositive of an If-Then Statement
- Congruence Statement
- Reflexive Property of Congruence and Equality
- Symmetric Property of Congruence and Equality
- Transitive Property of Congruence and Equality
- Properties of Equality
- Applying the Properties of Equality/Congrunce in Logical Arguements
- Types of Proofs
- Methods of Proof
- Proving or Disproving a Solution
- Mathematical Connections
- Identifying Related Mathematical Concepts
- Learning by Extension
- Generalizations
- Making a Generalization
- Testing a Generalization

Study fundamental topics in college-level algebra with emphasis on application.

Grasp core concepts of statistics such as probability distributions, approximations, and hypothesis-testing.

Pathways are a sequence of tutorials that help you learn a whole subject area, one concept at a time. Choose from multiple teachers and teaching styles.

The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 25 of Sophia's online courses for college credit. These courses are eligible to transfer to many different colleges and universities.