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Jan says that a rhombus is a parallelogram and that every parallelogram is also a rhombus. Is Jan correct?

YES

Question 2
Part B

Explain why or why not.

(4 points)

1 answer

Jan is partially correct in her statement. While it is true that a rhombus is a specific type of parallelogram, not every parallelogram is a rhombus.

Here are the explanations:

  1. Correct Part: A rhombus is indeed a parallelogram. Both shapes share certain defining properties – they have opposite sides that are parallel and equal in length, and their opposite angles are equal.

  2. Incorrect Part: However, not every parallelogram is a rhombus. A parallelogram only requires opposite sides to be equal and parallel, but the angles can vary. For instance, a rectangle is a type of parallelogram where all angles are right angles, but it does not have all sides equal, which is a requirement for a rhombus.

  3. Specific Definition: A rhombus specifically has all four sides of equal length. This characteristic distinguishes it from other types of parallelograms, such as rectangles and general parallelograms, which may not have equal sides.

  4. Conclusion: Therefore, Jan is mistaken in claiming that every parallelogram is a rhombus. While all rhombuses are parallelograms, the converse is not true.