What is a diamond ?

What is a diamond ?

a quadrangle as a rhombus stands out among the variety of geometric shapes.Even its very name is not typical to refer to quadrangles.Although the geometry of it occurs much less frequently than such simple shapes like circle, triangle, square or rectangle, it also can not be ignored.

Below are the definition of the properties and features of the rhombus.

Definition

Rhombus - a parallelogram having equal sides.Rhombus square called if all its angles.The most striking example is the diamond-shaped image of diamonds playing card suit on.In addition, the diamond often depicted in various emblems.An example of a rhombus in everyday life can serve Ballpark.

Properties

  1. opposite sides of the rhombus lie on parallel lines, and have the same length.
  2. intersection of the diagonals of the rhombus occurs at an angle of 90 ° at one point, which is their middle.
  3. diagonals of a rhombus divided angle from the top of which they came, in half.
  4. Based on the properties of a parallelogram, we can derive the su
    m of the squares of the diagonals.According to the formula, it is side raised to degree quadratic and multiplied by four.

Signs

We must clearly understand that any rhombus is a parallelogram, but at the same time is not any parallelogram has all the performance of the diamond.To distinguish between these two geometric shapes, you need to know the signs of a rhombus.Below are the characteristics of this geometric figure:

  1. any two sides with a common vertex are equal.
  2. diagonals intersect at an angle of 90 ° C.
  3. At least one diagonal divides the angles of the points of the vertices which it comes in half.

Formula area

basic formula:

  • S = (AC * BD) / 2

Based on the properties of a parallelogram:

  • S = (AB * HAB)

Based on the value of the angle between two adjacentthe 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 - area;
    • AB, AC, BD - the designation of the parties;
    • H - height;
    • r - radius of the circle;
    • sinα - sine alpha.

Perimeter

To calculate the perimeter of a rhombus, you just multiply the length of any of the parties at four.

picture Building

have some difficulties with the construction of a rhombus pattern.Even if you have already figured out that this diamond is not always clear how to build its image accurately and in compliance with the necessary proportions.

There are two ways of constructing a rhombus pattern:

  1. Build first one diagonal, then perpendicular to the second diagonal, and then connect the ends of the segments adjacent pairs of parallel sides of the diamond.
  2. Takeout first one side of the rhombus, then parallel to construct a segment equal in length, and connect the ends of these segments are also mutually parallel.

Be careful when building - if you make the length of the sides of the rhombus are the same, you do not get the diamond, and the square below.

See also article:

  • Find rhombus
  • area How to find a diagonal of the rhombus
  • How to find the direction of the rhombus