Answer this!
1. There can be more than one conditional, converse and inverse statement for
a conditional statement. True or False?
2. Match the notation of the statements shown below.
Connect it using a line.

Converse statement • • if not p, then not q
Contrapositive statement • • if p, then q
Inverse statement • • if not q, then not p

3. If the shape is a triangle, then the sum of the internal angles is 180 degrees.
Find the inverse statement.
a. If the shape is not a triangle, then the sum of the internal angles is not
equal to 180 degrees
b. If the sum of the interior angles is equal to 180 degrees, then it is not a
triangle
c. If the shape is a triangle, then the sum of the internal angles is not equal
to 180 degrees.
d. If the sum of the internal angles is not equal to 180 degrees, then it is
not a triangle.

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4. If a shape is closed, then it is a polygon. Identify the inverse statement for a
conditional statement
a. If it is a polygon, then the shape is closed
b. If the shape is not a polygon, then the shape is not closed
c. If the shape is not closed then it is not a polygon
d. If it is not a polygon, then the shape is closed.
5. Choose true/false against each statement.
Put a check on the column of
your answer.

True False

All rectangles are quadrilaterals.
All squares are polygons.
All quadrilaterals are rectangles.

Let's address each part of your request one by one:

### 1. True or False Statement:
**Statement**: There can be more than one conditional, converse, and inverse statement for a conditional statement.  
**Answer**: **False**  
- **Explanation**: For a given conditional statement, there is only one corresponding converse, inverse, and contrapositive statement.

### 2. Matching Notation of Statements:

| Statement Type             | Corresponding Notation               |
|----------------------------|--------------------------------------|
| **Converse statement**      | **if q, then p**                     |
| **Contrapositive statement**| **if not q, then not p**             |
| **Inverse statement**       | **if not p, then not q**             |

To visualize the connections:
- **Converse statement** should connect to "if q, then p"
- **Contrapositive statement** should connect to "if not q, then not p"
- **Inverse statement** should connect to "if not p, then not q"

### 3. Inverse Statement for the Given Conditional:
**Conditional Statement**: If the shape is a triangle, then the sum of the internal angles is 180 degrees.  
**Inverse Statement**: The correct option is **a**.  
- **Answer**: **a. If the shape is not a triangle, then the sum of the internal angles is not equal to 180 degrees**.

### 4. Inverse Statement for a Conditional Statement:
**Conditional Statement**: If a shape is closed, then it is a polygon.  
**Inverse Statement**: The correct option is **c**.  
- **Answer**: **c. If the shape is not closed, then it is not a polygon**.

### 5. True/False Statements:
**Statements**:

| Statement                           | True/False           |
|-------------------------------------|----------------------|
| All rectangles are quadrilaterals.  | **True**             |
| All squares are polygons.           | **True**             |
| All quadrilaterals are rectangles.  | **False**            |

### Summary:

- **1.** False  
- **2.** Match as listed.
- **3.** a. If the shape is not a triangle, then the sum of the internal angles is not equal to 180 degrees.  
- **4.** c. If the shape is not closed, then it is not a polygon.  
- **5.** True, True, False.

Would you like more details or have any questions?

### Relative Questions:
1. What is the contrapositive of the statement "If p, then q"?
2. Can a conditional statement be true if its converse is false?
3. How do you form the contrapositive of a conditional statement?
4. Are all polygons closed shapes?
5. Why is it false to say all quadrilaterals are rectangles?

### Tip:
When dealing with logical statements, remember that the truth of a conditional statement does not guarantee the truth of its converse or inverse.

1. There can be more than one conditional, converse and inverse statement for a conditional statement. True or False?
2. Match the notation of the statements shown below.
Converse statement • • if not p, then not q
Contrapositive statement • • if p, then q
Inverse statement • • if not q, then not p

3. If the shape is a triangle, then the sum of the internal angles is 180 degrees. Find the inverse statement.
a. If the shape is not a triangle, then the sum of the internal angles is not equal to 180 degrees
b. If the sum of the interior angles is equal to 180 degrees, then it is not a triangle
c. If the shape is a triangle, then the sum of the internal angles is not equal to 180 degrees.
d. If the sum of the internal angles is not equal to 180 degrees, then it is not a triangle.

4. If a shape is closed, then it is a polygon. Identify the inverse statement for a conditional statement
a. If it is a polygon, then the shape is closed
b. If the shape is not a polygon, then the shape is not closed
c. If the shape is not closed then it is not a polygon
d. If it is not a polygon, then the shape is closed.

5. Choose true/false against each statement.
All rectangles are quadrilaterals.
All squares are polygons.
All quadrilaterals are rectangles.

Explore conditional logic and how to identify converse, inverse, and contrapositive statements. This problem covers key geometry concepts like the triangle sum theorem and logical reasoning. Suitable for students in Grades 8-10.

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