Question
In 7-10, write whether each statement is tr 7. All rhombuses are rectangles. 9. Rhombuses are special parallelograms.
Ask by Morgan Li. in the United States
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
**7. False**
**9. True**
Solution
**7. All rhombuses are rectangles.**
- A **rectangle** is a quadrilateral with four right angles.
- A **rhombus** is a quadrilateral with four equal sides.
- For a rhombus to be a rectangle, it must also have four right angles. However, not every rhombus satisfies this condition.
- Thus, the statement \( \text{All rhombuses are rectangles} \) is **False**.
**9. Rhombuses are special parallelograms.**
- A **parallelogram** is a quadrilateral with both pairs of opposite sides parallel.
- Every rhombus has both pairs of opposite sides parallel (and all sides are equal).
- Hence, every rhombus is a parallelogram with the additional property of having four equal sides, making it a special case.
- Thus, the statement \( \text{Rhombuses are special parallelograms} \) is **True**.
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The Deep Dive
While it's tempting to think all rhombuses are rectangles because they both share the properties of parallelograms, that's a no-go! A rhombus has all sides equal and opposite angles equal, but its angles don’t have to be 90 degrees, which is a must for rectangles. So, statement 7 is false. On the other hand, rhombuses are indeed special parallelograms since they satisfy all the conditions of a parallelogram: opposite sides are equal, opposite angles are equal, and the diagonals bisect each other. So, statement 9 is true!