Indirect proofs are usually used when the wordcannotappears in the proof.
Example:Prove a triangle cannot have two right angles.
Assume a triangle can have two right angles. Then, using the Triangle Sum Theorem, 90+ 90 +x=180 degrees.
Using the angle addition property and the addition property of equality,x=0 (here lies your contradiction). But a
triangle must have three angles greater than zero degrees. Therefore, a triangle cannot have two right angles.
Additional Example:Prove
√
156 =4.
Assume
√
15 =4.Then, by squaring both sides, 15 = 16 .But 15 6 =16.Therefore,√
156 = 4
1.5. Relationships Within Triangles