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.

To solve this, we need to identify which of the given statements has a false **converse**. The **converse** of a conditional statement "If P, then Q" is "If Q, then P." Let's examine each statement and its converse.

### Statement A:
**Original:** "If \( m∠A = 90 \), then ∠A is a right angle."  
**Converse:** "If ∠A is a right angle, then \( m∠A = 90 \)."  
The converse of this statement is true because, by definition, a right angle always measures 90 degrees.

### Statement B:
**Original:** "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 the segment into two congruent parts."  
The converse is true because the midpoint always divides a segment into two equal parts.

### Statement C:
**Original:** "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**. Two angles can be supplementary (i.e., sum to 180°) without forming a linear pair. For example, two angles inside a triangle can be supplementary, but they are not a linear pair.

### Statement D:
**Original:** "If two angles are complementary, then the sum of their measures is 90°."  
**Converse:** "If the sum of two angles is 90°, then they are complementary."  
The converse is true because by definition, complementary angles add up to 90°.

### Conclusion:
The statement with a false converse is **Statement C**. The false converse is: "If two angles are supplementary, then they are a linear pair."

Would you like more details or further clarifications?

### Related Questions:
1. What is the difference between a conditional statement and its converse?
2. Can a converse of a true statement ever be false, and if so, why?
3. How do supplementary angles differ from a linear pair of angles?
4. What are contrapositive and inverse statements in logic?
5. Can you give examples of real-life situations involving linear pairs or supplementary angles?

### Tip:
Remember, a converse can be false even if the original statement is true. Always analyze the converse separately from the original statement.

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.

Discover how to identify which conditional statement has a false converse. Learn about logical reasoning in geometry, covering topics such as linear pairs, supplementary angles, and converse statements. This question is ideal for high school students (Grades 9-12) studying geometry and logic.

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