Write the converse, inverse, and contrapositive of the statement below. If the two angles are complementary, then the angles are acute. Converse: Inverse: Contrapositive:

Question

UpStudy AI · Accepted Answer

Certainly! Let's break down the original statement and then construct its converse, inverse, and contrapositive.

**Original Statement:**
- *If the two angles are complementary, then the angles are acute.*

Here, 
- **P**: The two angles are complementary.
- **Q**: The angles are acute.

### Converse:
The converse of a statement switches the hypothesis and the conclusion.

- **Converse:** *If the angles are acute, then the two angles are complementary.*

### Inverse:
The inverse of a statement negates both the hypothesis and the conclusion.

- **Inverse:** *If the two angles are not complementary, then the angles are not acute.*

### Contrapositive:
The contrapositive of a statement both switches and negates the hypothesis and the conclusion.

- **Contrapositive:** *If the angles are not acute, then the two angles are not complementary.*

**Summary:**

- **Converse:** If the angles are acute, then the two angles are complementary.
- **Inverse:** If the two angles are not complementary, then the angles are not acute.
- **Contrapositive:** If the angles are not acute, then the two angles are not complementary.
- **Converse:** If the angles are acute, then the two angles are complementary. - **Inverse:** If the two angles are not complementary, then the angles are not acute. - **Contrapositive:** If the angles are not acute, then the two angles are not complementary.

Write the converse, inverse, and contrapositive of the statement below. If the two angles are complementary, then the angles are acute. Converse: Inverse: Contrapositive:

Solución de tutoría real

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Other Questions