1. 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.

2. 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.

3. 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.

4. 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

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

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

7. 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.