Given: the cost of two items is more than $50. Use indirect reasoning to prove: If Jacky spends more than $50 to buy two items at a bicycle shop, then at least one of the items costs more than $25. Given: the cost of two items is more than $50. Prove: At least one of the items costs more than $25. Begin by assuming that the opposite is true. That is assume that neither item costs more than $25.

Given: the cost of two items is more than $50. Use indirect reasoning to prove: If Jacky spends more than $50 to buy two items at a bicycle shop, then at least one of the items costs more than $25. Given: the cost of two items is more than $50. Prove: At least one of the items costs more than $25. Begin by assuming that the opposite is true. That is assume that neither item costs more than $25. This means that both items cost $25 or less. This means that the two items together cost $50 or less. This contradicts the given information that the amount spent is more than $50. So the assumption that neither items cost more than $25 must be incorrect.

Therefore, at least one of the items costs more than $25. Use indirect reasoning to prove: If Jacky spends more than $50 to buy two items at a bicycle shop, then at least one of the items costs more than $25. Therefore, at least one of the items costs more than $25. This means that both items cost $25 or less. This means that the two items together cost $50 or less. This contradicts the given information that the amount spent is more than $50. So the assumption that neither items cost more than $25 must be incorrect.

Writing an indirect proof Step-1: Assume that the opposite of what you want to prove is true. Step-2: Use logical reasoning to reach a contradiction to the earlier statement, such as the given information or a theorem. Then state that the assumption you made was false. Step-3: State that what you wanted to prove must be true

Write an indirect proof: Assume has more than one right angle. That is assume are both right angles.

Write an indirect proof: If are both right angles, then According to the Triangle Angle Sum Theorem,. By substitution: Solving leaves:

Write an indirect proof: If: , This means that there is no triangle LMN. Which contradicts the given statement. So the assumption that are both right angles must be false.