Biconditional statements are reversible. Which of the following conditional statements can be written as a biconditional?
A.If you want to buy clothes, then you go to the mall.
B.If a number is divisible by 10, then it is divisible by 5.
C.If a polygon is a square, then it has four right angles.
D.If the measures of two angles add up to 90, then the angles are complementary.

To determine which conditional statement can be written as a **biconditional** (meaning both the statement and its converse are true), we must check if the converse of each statement is also true.

### Let's examine each option:

**A.** *If you want to buy clothes, then you go to the mall.*  
- **Converse**: If you go to the mall, then you want to buy clothes.  
  This is not necessarily true, as people may go to the mall for reasons other than buying clothes.  
  **Not biconditional.**

**B.** *If a number is divisible by 10, then it is divisible by 5.*  
- **Converse**: If a number is divisible by 5, then it is divisible by 10.  
  This is false, as numbers like 15 are divisible by 5 but not by 10.  
  **Not biconditional.**

**C.** *If a polygon is a square, then it has four right angles.*  
- **Converse**: If a polygon has four right angles, then it is a square.  
  This is false, as a rectangle also has four right angles but is not necessarily a square.  
  **Not biconditional.**

**D.** *If the measures of two angles add up to 90, then the angles are complementary.*  
- **Converse**: If two angles are complementary, then their measures add up to 90 degrees.  
  This is true, as complementary angles are defined by their sum being 90 degrees.  
  **This can be written as a biconditional.**

### Conclusion:
The correct answer is **D**: *If the measures of two angles add up to 90, then the angles are complementary.*

Would you like further details or have any questions?

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Here are 5 related questions to deepen understanding:
1. What is the difference between a conditional and biconditional statement?
2. Can all true conditional statements be made biconditional?
3. How do you write the converse of a conditional statement?
4. What does it mean if a conditional statement is "reversible"?
5. How are biconditional statements used in geometric proofs?

**Tip:** Always check the converse of a conditional statement to see if it holds when determining if it can be made biconditional.

Explore how to determine which conditional statements can be written as biconditional. This problem involves logical reasoning and geometric concepts like complementary angles. Suitable for students in Grades 9-12.

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