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. (4 points)
1 If two angles are supplementary, then they form a linear pair
2 Two angles form a linear pair if and only if they are supplementary
3 If two angles are not supplementary, then they do not form a linear pair
4 If two angles do not form a linear pair, then they are not supplementary
1 If two angles are supplementary, then they form a linear pair
This statement is the converse of the given conditional statement.
2 Two angles form a linear pair if and only if they are supplementary
This statement is the biconditional statement of the given conditional statement.
3 If two angles are not supplementary, then they do not form a linear pair
This statement is the contrapositive of the given conditional statement.
4 If two angles do not form a linear pair, then they are not supplementary
This statement is the inverse of the given conditional statement.
The correct matching of the statements is as follows:
Inverse: Statement 3 - If two angles are not supplementary, then they do not form a linear pair.
Converse: Statement 1 - If two angles are supplementary, then they form a linear pair.
Contrapositive: Statement 4 - If two angles do not form a linear pair, then they are not supplementary.
Biconditional: Statement 2 - Two angles form a linear pair if and only if they are supplementary.
To determine the correct statement for the inverse, converse, contrapositive, and biconditional statements of the given conditional statement, we need to understand their definitions:
1. Inverse: In the inverse statement, we negate both the hypothesis and conclusion of the original conditional statement.
2. Converse: The converse statement of a conditional statement swaps the hypothesis and conclusion.
3. Contrapositive: The contrapositive statement is formed by negating both the hypothesis and conclusion of the converse statement.
4. Biconditional: A biconditional statement is formed by combining the conditional statement and its converse statement using "if and only if."
Now, let's examine each option and match them with the corresponding type of statement:
1. If two angles are supplementary, then they form a linear pair.
- This matches the inverse of the given conditional statement.
2. Two angles form a linear pair if and only if they are supplementary.
- This matches the biconditional statement.
3. If two angles are not supplementary, then they do not form a linear pair.
- This matches the contrapositive of the given conditional statement.
4. If two angles do not form a linear pair, then they are not supplementary.
- This matches the converse of the given conditional statement.
To summarize:
- The correct statement for the inverse is option 1.
- The correct statement for the converse is option 4.
- The correct statement for the contrapositive is option 3.
- The correct statement for the biconditional is option 2.