If two angles do not form a linear pair, then
they are not supplementary
If two angles are supplementary, then they
form a linear pair
If two angles are not supplementary, then
they do not form a linear pair
Two angles form a linear pair if and only if
they are supplementary
Using the conditional statement below, match the correct statement to the inverse, converse, contrapositive and biconditional statement
If two angles form a linear pair, then they are supplementary.
Inverse: If two angles do not form a linear pair, then they are not supplementary.
Converse: If two angles are supplementary, then they form a linear pair.
Contrapositive: If two angles do not form a linear pair, then they are not supplementary.
Biconditional: Two angles form a linear pair if and only if they are supplementary.
Inverse: If two angles do not form a linear pair, then they are not supplementary.
Converse: If two angles are supplementary, then they form a linear pair.
Contrapositive: If two angles do not form a linear pair, then they are not supplementary.
Biconditional: Two angles form a linear pair if and only if they are supplementary.
To match the correct statements to the inverse, converse, contrapositive, and biconditional statement, we need to understand the definitions of each statement:
1. Inverse: The inverse of a conditional statement switches the hypothesis and the conclusion, and negates both. It can be written as "If two angles do not form a linear pair, then they are not supplementary."
2. Converse: The converse of a conditional statement switches the hypothesis and the conclusion. It can be written as "If two angles are supplementary, then they form a linear pair."
3. Contrapositive: The contrapositive of a conditional statement switches the hypothesis and the conclusion, and negates both. It can be written as "If two angles do not form a linear pair, then they are not supplementary."
4. Biconditional: A biconditional statement is a two-part statement that consists of a conditional statement and its converse connected by "if and only if" or "iff." It expresses that both the conditional statement and its converse are true. It can be written as "Two angles form a linear pair if and only if they are supplementary."
Now, let's match the statements:
- Inverse: "If two angles do not form a linear pair, then they are not supplementary."
- Converse: "If two angles are supplementary, then they form a linear pair."
- Contrapositive: "If two angles do not form a linear pair, then they are not supplementary."
- Biconditional: "Two angles form a linear pair if and only if they are supplementary."
Please note that the statements provided above are based on the conditional statement given in the question.