Of course! Let's analyze the given conditional statement and derive its related conditionals.
The given conditional statement is:
"If two angles are complementary, then they add to 90°."
To derive the related conditionals, we need to construct the converse, inverse, and contrapositive.
### Original Statement:
If two angles are complementary, then they add to 90°.
Form:
- Hypothesis (P): Two angles are complementary.
- Conclusion (Q): They add to 90°.
### 6. Converse:
The converse of a statement is formed by switching the hypothesis and the conclusion.
Original: If P, then Q.
Converse: If Q, then P.
For this statement:
- Original: If two angles are complementary, then they add to 90°.
- Converse: If two angles add to 90°, then they are complementary.
### 7. Inverse:
The inverse of a statement is formed by negating both the hypothesis and the conclusion.
Original: If P, then Q.
Inverse: If not P, then not Q.
For this statement:
- Original: If two angles are complementary, then they add to 90°.
- Inverse: If two angles are not complementary, then they do not add to 90°.
### 8. Contrapositive:
The contrapositive of a statement is formed by both switching and negating the hypothesis and the conclusion.
Original: If P, then Q.
Contrapositive: If not Q, then not P.
For this statement:
- Original: If two angles are complementary, then they add to 90°.
- Contrapositive: If two angles do not add to 90°, then they are not complementary.
### Summary:
1. Converse: If two angles add to 90°, then they are complementary.
2. Inverse: If two angles are not complementary, then they do not add to 90°.
3. Contrapositive: If two angles do not add to 90°, then they are not complementary.
These related conditionals are essential in logic and reasoning, particularly in mathematical proofs and problem-solving scenarios.
