It seems that your question is incomplete regarding which specific properties or aspects of the rectangle you want to explore. However, here are several key theorems and properties relating to rectangles that might support various statements or questions about rectangles:
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Theorem 1: Properties of Rectangles
- A rectangle is defined as a quadrilateral with four right angles.
- Opposite sides of a rectangle are equal in length and parallel.
- The diagonals of a rectangle are equal in length.
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Theorem 2: Pythagorean Theorem
- In a rectangle, the diagonals can be calculated using the Pythagorean theorem. If the lengths of the sides are \( a \) and \( b \), then the length of the diagonal \( d \) is \( d = \sqrt{a^2 + b^2} \).
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Theorem 3: Area of a Rectangle
- The area \( A \) of a rectangle can be calculated by multiplying its length \( l \) by its width \( w \), given by the formula \( A = l \times w \).
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Theorem 4: Perimeter of a Rectangle
- The perimeter \( P \) of a rectangle can be calculated using the formula \( P = 2(l + w) \).
If you have a specific theorem or question in mind that you would like to explore further, please provide more details so I can assist you effectively!