Indirect proof is a type of proof in which a statement to be proved is assumed false and if the assumption leads to an impossibility, then the statement assumed false has been proved to be true
Sum of 2n even numbers is even, where n > 0. Prove the statement using an indirect proof.
The first step of an indirect proof is to assume that 'Sum of even integers is odd.'
That is, 2 + 4 + 6 + 8 + . . . .+ 2n = an odd number
⇒ 2(1 + 2 + 3 + 4 + . . . + n) = an odd number ⇒ 2 × = an odd number
⇒ n(n + 1) = an odd number, a contradiction, because n(n + 1) is always an even number.
Thus, the statement is proved using an indirect proof.
Step 1: Assume â–³LMN has more than one right angle. That is, assume that angle L and angle M are both right angles.
Step 2: If M and N are both right angles, then m∠L = m∠M = 90
Step 3: m∠L + m∠M + m∠N = 180 [The sum of the measures of the angles of a triangle is 180.]
Step 4: Substitution gives 90 + 90 + m∠N = 180.
Step 5: Solving gives m∠N = 0.
Step 6: This means that there is no â–³LMN, which contradicts the given statement.
Step 7: So, the assumption that ∠L and ∠M are both right angles must be false.
Step 8: Therefore, â–³LMN has at most one right angle.