Which of the following statements has a false converse?

A.If *m*∠*A* = 90, then ∠*A* is a right angle.

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

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

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

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.

Which of the following statements has a false converse?

A. If ∠A = 90, then ∠A is a right angle.
B. If a point bisects a segment into two congruent parts, then it is midpoint.
C. If two angles are a linear pair, then they are supplementary.
D. If two angles are complementary, then the sum of their measures add up to 90.

Learn how to identify a false converse statement in geometry. This problem involves key concepts such as linear pairs, supplementary angles, and complementary angles. Suitable for students in Grades 8-10.

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