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