What is a rhombus? It is known that this is an equilateral quadrilateral, which is also a parallelogram. And if a rhombus has all the angles equal, then this figure can already be called a square. And all opposite sides of the rhombus are parallel.
What is a rhombus
Rhombus is an equilateral parallelogram. The word itself is of Greek origin and means "tambourine". These are today tambourines of a round shape, but earlier they were made in the form of a square. That is why the rhombus has such a name. It also has a name as a heraldic figure. Let's turn to Ushakov's dictionary. What is a rhombus? Compared to a square, it is a rhombus with equal angles. And also a square is a special case of a rhombus. Sometimes they even say that these figures can be compared.
Also associated with the rhombus is the image of the "tambourine" suit on cards used in gambling. This figure was also used for images on banners, flags and various coats of arms, but it is much less common than other geometric designs. And today the rhombus is also used forimages of a basketball field. We know what a rhombus is, but let's look at the properties and features of this figure.
Rhombus Properties
- Rhombus is represented by a parallelogram, all sides of which are opposite, equal and parallel.
- The diagonals of this mathematical construction intersect only at right angles and are divided in half at the point of intersection. That is, these diagonals divide the rhombus into four absolutely equal triangles.
- Angle bisectors are exactly the diagonals.
- The sum of the squares of the diagonals equals the square of the side multiplied by four.
- The vertices of the rectangle are the midpoints of the four sides of this construction called a rhombus.
- The diagonals of the figure are perpendicular to their axes of symmetry.
- A circle with a center lying at the intersection can be inscribed in any figure called a rhombus.
- What is the diagonal of a rhombus? This is the line that connects its corners.
Signs of a diamond
We learned what a rhombus is, but in addition to the properties of this figure, there are also signs. Any parallelogram will be a rhombus if it fulfills at least one of the following conditions:
- Two adjacent sides of a rhombus are equal with respect to each other.
- The diagonals of this mathematical construction can only intersect at right angles and nothing else.
- One of the diagonals necessarily bisects all its corners that it contains.
- And if we assume that weit is not known that the quadrilateral is a parallelogram, but it is known that the sides of the figure are equal, then we can confidently say: the quadrilateral is a rhombus.
- This is the part of the line that forms an angle equal to 90 degrees when crossing the opposite side.
- What is the height of the diamond? This is the part of the line that makes a 90 degree angle when it intersects the opposite side.
Rhombus area
We know what a rhombus is, what are its properties and signs, but how to find its area? To find the area of a rhombus, divide the product of the diagonals of this figure in half. Since a rhombus is the same parallelogram, the area of such a mathematical construction is equal to the product of the height and the length of its sides. In addition, the area of \u200b\u200ba figure can be found when calculating using formulas with adjacent sides or with the radius of an inscribed circle. The radius of an inscribed circle is expressed in terms of diagonals. To calculate the perimeter of a rhombus, multiply the length of one of the four sides by four.
And in order to depict this figure in the form of a picture, you must follow the instructions below. After all, when building this figure, many have difficulties. So, in order to accurately depict a rhombus, you should first draw the first diagonal, then perpendicular to the second, and finally connect the edges of the segments. You need to draw this figure very carefully and carefully so that instead of a rhombus you do not draw a square.
