• What is a diamond?

    Among the variety of geometric shapes, a quadrilateral such as a rhombus stands out prominently. Even its name itself is not typical of quadrilaterals. And although in geometry it occurs much less frequently than such simple shapes as a circle, triangle, square, or rectangle, it also cannot be ignored.

    Below are the definition, properties and characteristics of diamonds.

    Definition

    A rhombus is a parallelogram with equal sides. A rhombus is called a square if all its angles are right. The most striking example of a diamond is the image of a diamond suit on a playing card. In addition, the diamond is often depicted on various coats of arms. An example of a diamond in everyday life is the basketball field.

    Properties

    1. The opposite sides of the rhombus lie on parallel lines and have the same length.
    2. The intersection of the diagonals of the rhombus occurs at an angle of 90aboutat one point, which is their middle.
    3. Diagonal rhombus divide the corner, from the top of which they came out in half.
    4. Based on the properties of the parallelogram, you can derive the sum of the squares of the diagonals.According to the formula, it is equal to the side raised to a quadratic power and multiplied by four.

    Signs of

    We must clearly understand that any rhombus is a parallelogram, but at the same time, not every parallelogram has all the indicators of a rhombus. To distinguish these two geometric shapes, one needs to know the signs of a rhombus. The following are the characteristic features of this geometric shape:

    1. Any two sides with a common vertex are equal.
    2. Diagonals intersect at an angle of 90aboutFROM.
    3. At least one diagonal divides the corners, from the points of the vertices of which it comes out in half.

    Formula Square

    The basic formula:

    • S = (AC * BD) / 2

    Based on the properties of the parallelogram:

    • S = (AB * HAB)

    Based on the angle between the two adjacent sides of the rhombus:

    • S = AB2 * sinα

    If we know the length of the radius of a circle inscribed in a rhombus:

    • S = 4r2/ (sinα), where:
      • S is the area;
      • AB, AC, BD - designation of the parties;
      • H - height;
      • r is the radius of the circle;
      • sinα - sine alpha.

    Perimeter

    To calculate the perimeter of a rhombus, it is enough to multiply the length of any of its sides by four.

    Drawing pattern

    Some have difficulty building a diamond pattern. Even if you have already figured out what a rhombus is, it is not always clear how to build its drawing neatly and with the necessary proportions.

    There are two ways to build a diamond pattern:

    1. First, construct one diagonal, then a second diagonal perpendicular to it, and then connect the ends of the segments of the adjacent pairwise parallel sides of the rhombus.
    2. To set aside initially one side of the rhombus, then parallel to it to build a segment equal in length, and connect the ends of these segments also in pairs in parallel.

    Be careful when building - if in the figure you make the length of all sides of the rhombus the same, you will get not a rhombus, but a square.


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