The characteristic of the main square is the fact that they are formed by four sides, which have exactly the same measures. These sides are organized so that they form four angles of straight (90 °).
He square Is a basic geometric figure, object of study of the flat geometry, since it is a two-dimensional figure (which has width and height but lacks depth).
Squares are polygons. More concretely, they are polygons (a) quadrilaterals by having four sides, (b) equilateral by having sides that measure the same and (c) by angles having angles of the same amplitude.
These last two properties of the square (equilateral and equiangle) can be summarized in a single word: regular. This means that the squares are regular quadrilateral polygons.
Like the other geometric figures, the square has an area. This can be calculated by multiplying one of its sides by itself. For example, if we have a square that measures 4 mm, its area will be 16 mm 2 .
Outstanding Features of Squares
1- Number of sides and dimension
The squares are composed of four sides that measure the same. In addition, squares are two-dimensional figures, which means they have only two dimensions: width and height.
The basic feature of squares is that they have four sides. They are flat figures, so they are called two-dimensional.
2- Polygon
The squares are a polygon. This means that the squares are geometric figures delimited by a closed line formed by consecutive segments of line (closed polygonal line).
Specifically it is a quadrilateral polygon because it has four sides.
3- Equilateral polygon
A polygon is said to be equilateral when all sides have the same measure. This means that if one side of the square measures 2 meters, all sides will measure two meters.
The squares are equilateral, which means that all their sides measure the same.
In the image, a square with equal sides of 5 cm is shown.
4- Polygon equidangle
A polygon is said to be equidistant when all the angles forming the closed polygonal line have the same measure.
All squares consist of four right angles (ie, 90 ° angles), regardless of the angle measurements in particular: both a square of 2 cm x 2 cm and a square of 10 m x 10 m have four right angles.
All squares are equidangles because their angles have the same amplitude. That is, 90 °.
5- Regular polygon
When a polygon is equilateral and at the same time equidangle, this is considered to be a regular polygon.
Because the square has sides that measure the same and angles of equal amplitude, we can say that this is a regular polygon.
Squares have both sides of equal measure as angles of equal amplitude, so they are regular polygons.
In the previous image, a square with four sides of 5 cm and four angles of 90 ° is shown.
6- The area of a square
The area of a square is equal to the product of one side on the other side. Because the two sides have exactly the same measure, the formula can be simplified by saying that the area of this polygon is equal to one of its sides squared, ie (side) 2 .
Some examples of calculating the area of a square are:
- Square with sides of 2 m: 2 m x 2 m = 4 m 2
- Squares with sides of 52 cm: 52 cm x 52 cm = 2704 cm 2
- Square with sides of 10 mm: 10 mm x 10 mm = 100 mm 2
The square presented in the image has sides of 5 cm.
Your area will be the product of 5 cm x 5 cm, or what is the same (5 cm) 2
In this case, the square area is 25 cm 2
7- The squares are parallelograms
Parallelograms are a type of quadrilateral having two pairs of parallel sides. This means that a pair of sides faces each other, while the other pair.
There are four types of parallelograms: rectangles, rhombuses, rhomboids, and squares.
Squares are parallelograms because they have two pairs of sides that are parallel.
The sides (a) and (c) are parallel.
The sides (b) and (d) are parallel.
8- The opposite angles are congruent and the consecutive angles are complementary
That two angles are congruent means that they have the same amplitude. In this sense, as a square have all the angles of the same amplitude, we can say that the opposite angles are congruent.
The fact that two consecutive angles are complementary means that the sum of these two is equal to a flat angle (one having an amplitude of 180 °).
The angles of a square are right angles (90 °), so their sum is 180 °.
9- They are constructed from a circumference
To construct a square, a circle is drawn. Subsequently, it is proceeded to draw two diameters on this circumference; These diameters must be perpendicular, forming a cross.
Once the diameters have been drawn, we will have four points where the line segments cut the circumference. If these four points are joined, a square will result.
10- The diagonals are cut at their midpoint
Diagonals are straight lines that are drawn from one angle to another that is opposite. In a square, you can draw two diagonals. These diagonals will intersect at the midpoint of the square.
In the image, the dotted lines represent the diagonals. As you can see, these lines cross exactly in the middle of the square.
References
- Square. Retrieved on July 17, 2017, from en.wikipedia.org
- Square and its properties. Retrieved on July 17, 2017, from mathonpenref.com
- Properties of Rhombuses, Rectangels and Squares. Retrieved on July 17, 2017, from dummies.com
- The properties of a square. Retrieved on July 17, 2017, from coolmth.com
- Square. Retrieved on July 17, 2017, from onlinemschool.com
- Properties of Squares. Retrieved on July 17, 2017, from brlliant.org.