Let's break down the task in the image and ensure everything is correct:

The given statement is:

"Two angles that form a linear pair are supplementary."

a) Write the statement as a conditional.

This is already correctly answered:

• "If two angles form a linear pair, then they are supplementary."

b) Write the converse of your statement.

You wrote:

• "If two angles are supplementary, then they form a linear pair."

This is incorrect because not all supplementary angles form a linear pair. Supplementary angles only need to sum to 180°, but they don't have to be adjacent. For example, two angles of 120° and 60° that are not adjacent can still be supplementary but don’t form a linear pair.

Correct version of b):

• "If two angles are supplementary, then they do not necessarily form a linear pair." (since the converse is false, we can add this observation)

c) Write the statement as a biconditional.

A biconditional statement is true only when both the conditional and its converse are true. Since the converse in part (b) is false, the biconditional cannot hold.

Therefore, the correct response is:

• "It is not possible to write the statement as a biconditional because the converse is false. (e.g., two angles can be supplementary without forming a linear pair, as mentioned earlier)."

Would you like further details on any part of the explanation?

5 Related Questions:

1. What makes angles supplementary?
2. What is the difference between a linear pair and supplementary angles?
3. How can you prove that two angles form a linear pair?
4. Why does the converse of the original statement fail?
5. Can you find other counterexamples where the converse of a statement is false?

Tip:

When writing biconditional statements, always ensure that both the original and the converse of the conditional statement are true.