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Geometric Proofs

Indirect Proof



The second important kind of geometric proof is indirect proof. In an indirect proof, instead of showing that the conclusion to be proved is true, you show that all of the alternatives are false. To do this, you must assume the negation of the statement to be proved. Then, deductive reasoning will lead to a contradiction: two statements that cannot both be true. A contradiction shows that the assumption made earlier is impossible, and therefore false. Thus, the statement to be proved must be true, because its negation is false. Below is a sample indirect geometric proof.

Given: Triangle ABC is an isosceles triangle with vertex angle A
Prove: Angles 1 and 2 are congruent