The question to ask is, "What if that statement is not true?".When is the right time to try an indirect proof or proof by contradiction? When the statement to be proven true can be questioned: "What if interior angles of triangles do not add to 180 °?" Try to prove that when you fail, you have succeeded! #Simple seps compared to accu rip how to#In all three cases, begin by presuming the opposite of the statement to be the case: "Assume for the sake of contradiction that the two squares are not similar figures …" "Let's assume for the moment that the angle bisector of an equilateral △ is not a median …" "If we assume the statement is false, then the sum of interior angles of a △ is more or less than 180 °" How To Do An Indirect Proof Try to come up with the indirect proof statement for each yourself before looking ahead. Prove: The sum of interior angles of a △ is 180 ° Given: An equilateral △ and an angle bisector from any vertex Prove: The two squares are similar figures Restate each as the beginning of a proof by contradiction: Here are three statements lending themselves to indirect proof. You cannot say more or less than that for the initial assumption. Then you have to make certain you are saying the opposite of the given statement. "Let us suppose that the statement is false …"Īha, says the astute reader, we are in for an indirect proof, or a proof by contradiction."If we momentarily assume the statement is false …"."Assuming for the sake of contradiction that …".Most mathematicians do that by beginning their proof something like this: You first need to clue the reader in on what you are doing. Geometricians such as yourself can get hung up on the very first step, because you have to word your assumption of falsity carefully. If you find the contradiction to your attempt to prove falsity, then the opposite condition (the original statement) must be true.Work hard to prove it is false until you bump into something that simply doesn't work, like a contradiction or a bit of unreality (like having to make a statement that "all circles are triangles," for example). Here are the three steps to do an indirect proof: The three steps seem simple, much as a one-page cartoon diagram makes assembling furniture seem simple. To move through indirect proof logic, you need real confidence and deep content knowledge. I could not prove it was false, so it must be true." Indirect Proof Steps You are subtly intending to fail, so that you can then step back and say, "I did my best to show it was false. Rather than attack the problem head-on, as with a direct proof, you go through some other steps to try to prove the exact opposite of the statement. Indirect ProofĪn indirect proof can be thought of as "the long way around" a problem. You did not prove it directly you proved it indirectly, by contradiction. If you "fail" to prove the falsity of the initial proposition, then the statement must be true. The "indirect" part comes from taking what seems to be the opposite stance from the proof's declaration, then trying to prove that. Indirect proof in geometry is also called proof by contradiction.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |