If you have studied geometry, you are familiar with writing proofs for theorems. Such proofs either are written in the form of columns (the classic method of writing proofs) or explained in the form of a paragraph. The latter, which uses complete sentences, is a more informal way of writing the proof. This is in contrast to the usual twocolumn proof, where a statement is given in one column and the proof in another column beside it.

State all the parts of the theorem, assuming the reader knows little about it.

Remember there are many ways of stating any proof and several ways of presenting your argument.

Make a sentence and then back it up with a justification or a mathematical reason to confirm or prove it true.

Keep your reason or justification as easy and simple to understand as possible. Don't fuss about perfect wording. Make your statements clear, and support each one with a legal and valid reason.

Pretend you are talking or explaining to someone who does not have much mathematical knowledge and does not know the facts present in the given part of the theorem.

Measure the quality of your proof by explaining it to someone who has not taken geometry. If the person can understand the proof by reading your paragraph, you can be sure that you have written an effective paragraph proof.