Curated OER
Euclidean Direct Proofs
Learning how to prove theorems in geometry can be challenging. This resource explains what a proof is, and the different styles for proofs. It also contains links to web-based practice problems that help guide learners though example...
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Faq About Proofs
This site provides links to questions sent in to Dr. Math about proofs. Topics covered include what proofs are, how to understand them, and how to build them, and much more. Be sure to click on the links which you believe may be helpful.
Oswego City School District
Regents Exam Prep Center: Writing a Proof: Direct Euclidean Proofs
This site is a look into the world of geometric proofs. You'll learn what a proof is and about the different types of proofs. Try the practice page to check your understanding. Teachers can check out the teacher resources for lesson and...
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Two Column Proofs
A response to an inquiry of how to prove a two column geometric proof problem at the Math Forum. This site gives a description of what a makes a proof and an example of a two column proof.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Building Two Column Proofs
Use this site to find details of how to construct a two column proof. Dr. Math responds to a question posed by a student and details the reasons for the order of steps and shows two different ways to do the same proof.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Order of a Proof
The site gives a diagram of steps to a proof. Dr. Math explains why the step order of a proof is important.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: The Value of Two Column Proofs
This site explains why we prove things. The explanation gives real world scenarios and an everyday example of why we should learn how to prove things.
CK-12 Foundation
Ck 12: Geometry: Two Column Proofs
[Free Registration/Login may be required to access all resource tools.] Write two-column proofs.
CK-12 Foundation
Ck 12: Geometry: Proofs Study Guide
[Free Registration/Login may be required to access all resource tools.] This study guide reviews proofs: algebraic proof, properties of congruence, and geometric proofs (two-column).
CK-12 Foundation
Ck 12: Geometry: Two Column Proofs Intermediate
[Free Registration/Login may be required to access all resource tools.] This concept teaches students how to write two-column proofs, and provides proofs for the Right Angle Theorem, Same Angle Supplements Theorem, and Vertical Angles...
Sophia Learning
Sophia: Types of Proofs: Lesson 3
This lesson will introduce flow chart proofs, paragraph proofs, and two-column proofs, and explain the similarity and differences between the different types of proofs. It is 3 of 5 in the series titled "Types of Proofs."
Wolfram Research
Wolfram Math World: Two Column Proof
MathWorld gives a discussion of the use of two-column proofs by high school and middle school students and its relevance to mathematicians.