A rhombus is not always a rectangle, but it can be. To understand why, let’s first define what a rhombus and a rectangle are.
A rhombus is a quadrilateral with all sides of equal length. Its opposite sides are parallel, and its opposite angles are equal. A rectangle, on the other hand, is also a quadrilateral with all angles equal to 90 degrees. Its opposite sides are parallel, and its adjacent sides are equal in length.
Now, let’s consider the properties of a rhombus. Since a rhombus has all sides of equal length, its diagonals bisect each other at right angles. This means that the diagonals of a rhombus divide it into 4 congruent right triangles. Therefore, a rhombus can be seen as a combination of 4 right triangles.
Next, let’s look at the properties of a rectangle. A rectangle has all angles equal to 90 degrees, which means that its opposite angles are supplementary, adding up to 180 degrees. This property is not shared by a rhombus, as its opposite angles are not necessarily supplementary.
So, is a rhombus always a rectangle? The answer is no. A rhombus can only be a rectangle if it satisfies the additional condition of having all angles equal to 90 degrees. In other words, if a rhombus has all angles equal to 90 degrees, then it is also a rectangle.
To illustrate this, let’s consider an example. Imagine a rhombus where all sides are equal in length, but its angles are not all 90 degrees. In this case, the rhombus would not be a rectangle, as it does not satisfy the condition of having all angles equal to 90 degrees.
A rhombus is not always a rectangle. A rhombus can only be a rectangle if it has all angles equal to 90 degrees. Otherwise, a rhombus and a rectangle are two distinct quadrilaterals with different properties.