How Do You Write an Indirect Proof?

How Do You Write an Indirect Proof?

In mathematics, write indirect proofs by first assuming the opposite of the statement to be proven to be true. Then, try to prove the opposite of one of the given facts based on that assumption. Rather than directly proving something to be false, indirect proofs work by proving that something cannot be true, therefore, it must be false.

  1. Assume the opposite of what you need to prove

    Indirect proofs commonly deal with proving that something is not equal, similar or perpendicular. The first step in writing an indirect proof is to assume the exact opposite of what you seek to prove is true. For instance, if the task is to prove that two lines are not equal in length, assume that they are equal.

  2. Work through the problem

    Based on the assumption that the opposite of the statement is true, work through the problem in such a manner that the results contradict any one of the given facts. For instance, if it is given that two lines are not equal, the task is to come to the point where it shows that the lines are actually equal.

  3. Finish the proof

    Once a contradiction is reached, finish the proof. State that since the assumption leads to a contradiction, the assumption must be false; thus, the original statement is true.