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Can A Rhombus Have A Right Angle?

prove that diagonals of rhombus bisect each other at right angle
prove that diagonals of rhombus bisect each other at right angle from www.meritnation.com

For many people, geometry can be a challenging subject. But when it comes to understanding shapes, there are a few basic rules that everyone should know. One of the most common questions asked is whether a rhombus can have a right angle. In this article, we will explore the answer to this question and provide a comprehensive explanation in layman's terms.

What is a Rhombus?

Before we delve into the question of whether a rhombus can have a right angle, let's first define what a rhombus is. A rhombus is a quadrilateral with all four sides of equal length. It is also known as a diamond or a lozenge. The opposite angles of a rhombus are equal, and the diagonals bisect each other at right angles.

Can a Rhombus Have a Right Angle?

The answer to this question is no, a rhombus cannot have a right angle. This is because all four sides of a rhombus are of equal length, and the opposite angles are equal. If one angle were to be a right angle, then the opposite angle would also have to be a right angle. This would mean that the rhombus would essentially become a square.

Another way to think about this is to consider the properties of a rhombus. The diagonals of a rhombus bisect each other at right angles. If one angle were to be a right angle, then the diagonals would be perpendicular to each other. However, since the diagonals of a rhombus are of equal length, they cannot be perpendicular to each other unless they are also of equal length.

Proof:

We can prove this mathematically as well. Let's assume that one angle of a rhombus is a right angle. We know that the opposite angle is also a right angle. Let's call the length of the sides of the rhombus "a".

Using the Pythagorean theorem, we can find the length of the diagonals:

d2 = a2 + a2

d2 = 2a2

d = a x √2

Since the diagonals are of equal length in a rhombus, we can equate them:

a x √2 = a x √2

This means that a = 0, which is not possible. Therefore, a rhombus cannot have a right angle.

What About a Square?

As we mentioned earlier, if a rhombus has a right angle, it essentially becomes a square. A square is a special case of a rhombus, with all four sides of equal length and all four angles equaling 90 degrees. So, if you are looking for a shape with a right angle, a square is a better choice than a rhombus.

Conclusion

In conclusion, a rhombus cannot have a right angle. This is because all four sides of a rhombus are of equal length, and the opposite angles are equal. If one angle were to be a right angle, then the rhombus would essentially become a square. It's important to understand the properties of shapes, as they can help with problem-solving and understanding geometric concepts.

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