:if compangles do not total \( 90^{\circ} \), then th complementry. 12. If a line bisects a segment, then the segment is divided into two congruent parts. Converse: If I do not go, then it rains Inverse: If it does rain, then I will go Contrapositive: If I gor then it does not 13. Ifit rains, then I will not go.

It looks like you're working on understanding conditional statements and their corresponding converse, inverse, and contrapositive forms. You've provided two different types of conditional statements: 1. **Geometric Statement:** - **Original Statement:** If a line bisects a segment, then the segment is divided into two congruent parts. 2. **Personal Statement:** - **Original Statement:** If it rains, then I will not go. Let's break down each statement individually to identify their converse, inverse, and contrapositive forms. --- ## 12. Geometric Statement **Original Statement:** - *If a line bisects a segment, then the segment is divided into two congruent parts.* **a. Converse:** - *If the segment is divided into two congruent parts, then a line bisects the segment.* **b. Inverse:** - *If a line does not bisect a segment, then the segment is not divided into two congruent parts.* **c. Contrapositive:** - *If the segment is not divided into two congruent parts, then the line does not bisect the segment.* **Explanation:** - **Converse** switches the hypothesis and conclusion. - **Inverse** negates both the hypothesis and conclusion. - **Contrapositive** switches and negates both the hypothesis and conclusion. Importantly, the contrapositive of a statement always has the same truth value as the original statement. --- ## 13. Personal Statement **Original Statement:** - *If it rains, then I will not go.* **a. Converse:** - *If I do not go, then it rains.* **b. Inverse:** - *If it does not rain, then I will go.* **c. Contrapositive:** - *If I go, then it does not rain.* **Explanation:** - **Converse**: Switches the roles of the two parts. - **Inverse**: Negates both parts of the original statement. - **Contrapositive**: Switches and negates both parts, maintaining the logical equivalence to the original statement. --- **Important Notes:** - **Converse** and **inverse** do not necessarily hold the same truth value as the original statement. They are separate statements that need their own evaluation. - **Contrapositive**, however, is always logically equivalent to the original statement. If the original statement is true, the contrapositive is also true, and vice versa. --- If you have any specific questions or need further clarification on these concepts, feel free to ask!