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.
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.
- The opposite sides of the rhombus lie on parallel lines and have the same length.
- The intersection of the diagonals of the rhombus occurs at an angle of 90aboutat one point, which is their middle.
- Diagonal rhombus divide the corner, from the top of which they came out in half.
- 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.
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:
- Any two sides with a common vertex are equal.
- Diagonals intersect at an angle of 90aboutFROM.
- At least one diagonal divides the corners, from the points of the vertices of which it comes out in half.
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.
To calculate the perimeter of a rhombus, it is enough to multiply the length of any of its sides by four.
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:
- 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.
- 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.