Definition of Indirect Proof
Examples of Indirect Proof
Solved Example on Indirect Proof
Prove the following statement using an indirect proof:
ΔLMN has at most one right angle.
Step 1: Assume ΔLMN 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 ΔLMN, which contradicts the given statement.
Step 7: So, the assumption that ∠L and ∠M are both right angles must be false.
Step 8: Therefore, ΔLMN has at most one right angle.
Related Terms for Indirect Proof