The converse of a statement is formed by swapping its hypothesis and conclusion. We need to determine which of these statements has a false converse. Let's examine each one:

1. Statement A: If ∠A = 90, then ∠A is a right angle.

   • Converse: If ∠A is a right angle, then ∠A = 90.
   • This converse is true because by definition, a right angle always measures 90 degrees.

2. Statement B: If a point bisects a segment into two congruent parts, then it is the midpoint.

   • Converse: If a point is the midpoint, then it bisects a segment into two congruent parts.
   • This converse is true because the midpoint of a segment always divides it into two equal parts.

3. Statement C: If two angles are a linear pair, then they are supplementary.

   • Converse: If two angles are supplementary, then they are a linear pair.
   • This converse is false because two angles can be supplementary (sum to 180 degrees) without being adjacent (i.e., they do not have to form a linear pair).

4. Statement D: If two angles are complementary, then the sum of their measures add up to 90.

   • Converse: If the sum of two angles is 90, then they are complementary.
   • This converse is true because complementary angles are defined as two angles whose measures add up to 90 degrees.

Conclusion: The statement with a false converse is Statement C.

Would you like more details on any of these statements? Here are some related questions:

1. What is the definition of a converse statement?
2. How do you determine if a converse is true or false?
3. Can a statement and its converse both be false?
4. What is an example of a true statement with a false converse outside geometry?
5. How does the concept of biconditional statements relate to converses?

Tip: Always check the converse of a statement separately to verify its truth, as it may not always hold true even if the original statement is true.