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Vhat is the smallest number of righ angles each of the following shape can have? a) Square b) Parallelogram

Ask by Craig Frazier. in the United Kingdom
Jan 20,2025

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- **a) Square:** 4 right angles - **b) Parallelogram:** 0 right angles

Solución

Let's analyze each shape to determine the smallest number of right angles they can have. ### a) Square **Definition:** A square is a special type of rectangle and rhombus. It is a quadrilateral with four equal sides and four equal angles. **Properties:** - All four angles in a square are right angles (90 degrees). **Conclusion:** A square **must** have all four angles as right angles. Therefore, the smallest (and only) number of right angles a square can have is **4**. --- ### b) Parallelogram **Definition:** A parallelogram is a quadrilateral with two pairs of parallel sides. **Properties:** - Opposite angles in a parallelogram are equal. - Consecutive angles are supplementary (add up to 180 degrees). - A parallelogram **does not** necessarily have right angles unless it is a rectangle. **Scenarios:** 1. **No Right Angles:** Consider a rhombus that is not a square. None of its angles are 90 degrees. 2. **With Right Angles:** If a parallelogram has right angles, it becomes a rectangle (or a square, which is a special case of a rectangle). **Conclusion:** A general parallelogram can have as few as **0** right angles. This occurs in shapes like rhombuses that are not squares. --- **Summary:** - **a) Square:** 4 right angles - **b) Parallelogram:** 0 right angles

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The Deep Dive

A square is a special type of rectangle and has four right angles, making it the shape with the maximum number of right angles for any quadrilateral. However, it’s worth noting that in terms of the minimum number of right angles, a square holds that distinction as well—there can’t be fewer than four in a perfect square! For a parallelogram, the smallest number of right angles it can have is two. This occurs in the case of a rectangle, which is a specific type of parallelogram. In contrast, other parallelograms can have zero right angles (like rhombuses), but the minimum, if we’re being technical, is indeed two.

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