Explain why a rectangle is a convex quadrilateral.

Answer

To explain why a rectangle is a convex quadrilateral, we can follow these steps:

### Step-by-Step Solution:

1. **Definition of Convex Quadrilateral**:
A convex quadrilateral is defined as a four-sided figure where all interior angles are less than 180 degrees, and the diagonals lie entirely within the shape.

2. **Properties of a Rectangle**:
A rectangle is a type of quadrilateral where all four angles are right angles (90 degrees).

3. **Checking the Angles**:
Since each angle in a rectangle is 90 degrees, we can confirm that:
- 90 degrees is less than 180 degrees.
Therefore, all angles in a rectangle satisfy the first property of a convex quadrilateral.

4. **Checking the Diagonals**:
In a rectangle, the diagonals connect opposite corners and lie completely within the shape.
- This means that the diagonals do not extend outside the rectangle.
Thus, the second property of a convex quadrilateral is also satisfied.

5. **Conclusion**:
Since both properties of a convex quadrilateral are satisfied (all angles are less than 180 degrees and the diagonals lie within the shape), we can conclude that a rectangle is indeed a convex quadrilateral.

### Final Statement:
Therefore, a rectangle is a convex quadrilateral because all its angles are less than 180 degrees, and its diagonals lie entirely within the shape.

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