One diamond it is a polygon which has four congruent sides. Therefore, the diamond It is formed by straight segments, called sides of the polygon, which meet only at the ends. These straight line segments end up forming a closed figure and their sides do not intersect at any time.
To be diamond, in addition to having all congruent sides, the geometric figure must have exactly four sides. This classifies the diamond like quadrilateral.
In addition, the diamonds are also parallelograms, for if a quadrilateral has all congruent sides, the opposite sides are parallel.
elements of a diamond
sides: These are the straight segments that limit the polygon;
vertices: are the meeting points between two sides;
internal angles: angles between two sides in the inner region of the polygon;
diagonals: Line segments that connect two vertices and that are not sides. They are also defined as straight line segments that connect two non-consecutive vertices.
Properties of parallelograms
As said, the diamonds are parallelograms and therefore all the properties below are valid for them.
Opposite angles of a parallelogram are congruent;
Opposite sides of a parallelogram are congruent;
The sum of the adjacent angles of a parallelogram results in 180°;
The diagonals of a parallelogram intersect at their midpoints.
The property arising from the fact that the diamond being a quadrilateral is only one and guarantees the following:
“The sum of the inside angles of a diamond equals 360°.”
Specific property of diamonds
Diamonds are parallelograms that have four equal sides. This additional condition also guarantees one more property:
“The diagonals of a diamond are perpendicular"
Thus, we can say that the diagonals of a diamond form an angle of 90° to each other.
By Luiz Paulo Moreira
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/o-que-e/matematica/o-que-e-losango.htm