if two angles do not form a linear pair, then they are not supplementary
contrapositive
biconditional
inverse
converse
inverse
The contrapositive of the given statement is: "If two angles are supplementary, then they form a linear pair."
The biconditional statement is: "Two angles form a linear pair if and only if they are supplementary."
The inverse of the given statement is: "If two angles form a linear pair, then they are supplementary."
The converse of the given statement is: "If two angles are not supplementary, then they do not form a linear pair."
To determine which of the given options (contrapositive, biconditional, inverse, or converse) represents the statement "if two angles do not form a linear pair, then they are not supplementary," we need to understand the meaning of each term in logic.
1. Contrapositive: The contrapositive of a conditional statement switches the position of the hypothesis (if part) and the conclusion (then part) and negates both. In this case, the conditional statement is "if two angles do not form a linear pair, then they are not supplementary." Its contrapositive would be "if two angles are supplementary, then they form a linear pair."
2. Biconditional: A biconditional statement is when two conditional statements are true at the same time. It uses the phrase "if and only if" to express this relationship. In this case, the biconditional statement would be "two angles do not form a linear pair if and only if they are not supplementary."
3. Inverse: The inverse of a conditional statement negates both the hypothesis and the conclusion of the original statement. In this case, the original statement is "if two angles do not form a linear pair, then they are not supplementary." Its inverse would be "if two angles form a linear pair, then they are supplementary."
4. Converse: The converse of a conditional statement switches the position of the hypothesis and the conclusion without negating them. In this case, the original statement is "if two angles do not form a linear pair, then they are not supplementary." Its converse would be "if two angles are not supplementary, then they do not form a linear pair."
Now let's evaluate each option:
- The contrapositive is not the correct representation because it has the opposite hypothesis and conclusion, but both are negated.
- The biconditional statement is not the correct representation because it expresses the condition where both angles are not supplementary and do not form a linear pair, which is not what the original statement implies.
- The inverse is not the correct representation because it negates both the hypothesis and conclusion in the opposite way.
- The converse is the correct representation because it switches the positions of the hypothesis and conclusion without negating them.
So, the correct answer is the converse.