A paragraph proof is a type of proof a student in geometry class might write out to prove that something about a diagram is true based on the initial given evidence and the standard theorems and postulates learned in the class.

There are two ways to write a geometry proof. One method is the paragraph proof, and the other method is the two-column proof. Generally speaking, the two-column proof is the preferred method, because it clearly organizes a statement and reason in the same row. A paragraph proof attempts to take the two-column proof and write it out in prose format, using complete sentences and possibly multiple paragraphs. This is not the preferred way to write a proof in geometry class, because it tends to accidentally leave out information or to be overly wordy to explain something clearly.

For example, a two-column proof might say that angle A is congruent to angle B in the statement column. The reason column could simply say "Theorem 2-7." The person writing out the proof might decide to write out that theorem, but it isn't necessary. The paragraph version of the same proof might say something like the following: "Based on theorem 2-7, which states that if two angles are supplements of congruent segments, the two angles are congruent, angle A is congruent to angle B."