You diamonds are flat geometric figures formed by four sides that have equal measures. They are polygons because its sides are formed by straight segments that are found only at the ends, so they have all the characteristics and properties that the polygons possess.
Diamond elements
all convex polygon – therefore, every diamond - has the following elements:
sides: diamonds have four sides;
vertices: the meeting points between two sides;
diagonals: the straight lines connecting two non-consecutive points. Diamonds have two diagonals;
internal angles: are the angles that are inside the diamond and are formed by two consecutive sides;
outside angles: are the angles that are outside the diamond.
Properties inherited from parallelograms
all diamond is also a parallelogram, that is, a figure that has four sides, the opposite sides being parallel. The following properties apply to any parallelogram, including the diamonds.
the opposite sides of a diamond they are parallel and congruent, that is, they have the same measure;
The opposite angles of a diamond are congruent;
Adjacent angles are supplementary. This means that the sum of these angles equals 180°;
In diamonds, the sum of an inside angle and the outside angle adjacent to it always results in 180°;
the diagonals of a diamond lie at their midpoints;
The sum of the interior angles of any polygon, including the diamonds, always equals 360°.
Specific property of diamonds
The diagonals of a diamond are perpendicular.
This property is also verified in the squares, which are also diamonds, as they are quadrilaterals that have all congruent sides and all their angles measure 90°.
By Luiz Paulo Moreira
Graduated in Mathematics
