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In a parallelogram, the diagonals are eq...

In a parallelogram, the diagonals are equal ( T / F )

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To determine whether the statement "In a parallelogram, the diagonals are equal" is true or false, we can analyze the properties of parallelograms and their diagonals. ### Step-by-Step Solution: 1. **Understanding Parallelograms**: A parallelogram is a four-sided figure (quadrilateral) where opposite sides are parallel and equal in length. 2. **Properties of Diagonals in Parallelograms**: In general, the diagonals of a parallelogram bisect each other. This means that they cut each other into two equal parts, but this does not necessarily mean that the diagonals themselves are equal. 3. **Special Cases**: The diagonals of a parallelogram are equal only in specific cases: - When the parallelogram is a rectangle (where all angles are 90 degrees). - When the parallelogram is a square (which is a special case of a rectangle). 4. **Conclusion**: Since not all parallelograms have equal diagonals (for example, a rhombus has diagonals that are not equal), the statement "In a parallelogram, the diagonals are equal" is **False**. ### Final Answer: **False** - In a parallelogram, the diagonals are not equal except in the special cases of rectangles and squares. ---
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