- Squares highlights
- 1- Number of sides and dimension
- 2- Polygon
- 3- equilateral polygon
- 4- Equiangular polygon
- 5- Regular polygon
- 6- The area of a square
- 7- Squares are parallelograms
- 8- The opposite angles are congruent and the consecutive ones are complementary
- 9- They are built from a circumference
- 10- The diagonals intersect at their midpoint
- References
The characteristic of the main square is the fact that it is made up of four sides, which have exactly the same measurements. These sides are arranged so that they form four right angles (90 °).
The square is a basic geometric figure, object of study of plane geometry, since it is a two-dimensional figure (which has width and height but lacks depth).
The squares are polygons. More specifically, they are polygons (a) quadrilateral because they have four sides, (b) equilateral because they have sides that measure the same and (c) equiangles because they have angles with the same amplitude.
These last two properties of the square (equilateral and equiangular) can be summed up in a single word: regular. This means that the squares are regular quadrilateral polygons.
Like 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 would be 16 mm 2.
Squares highlights
1- Number of sides and dimension
The squares are made up of four sides that measure the same. Also, squares are two-dimensional figures, which means that they only have two dimensions: width and height.
2- Polygon
The squares are a polygon. This means that the squares are geometric figures delimited by a closed line formed by consecutive line segments (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 is 2 meters, all sides will measure two meters.
4- Equiangular polygon
A polygon is said to be equiangular when all the angles that the closed polygonal line forms have the same measure.
All squares are made up of four right angles (that is, 90 ° angles), regardless of the measures of the particular angle: both a 2 cm x 2 cm square and a 10 m x 10 m square have four right angles.
5- Regular polygon
When a polygon is both equilateral and equiangular, it is considered to be a regular polygon.
Because the square has sides that measure the same and angles of equal width, it can be said that this is a regular polygon.
Squares have both sides of equal measure and angles of equal width, so they are regular polygons.
In the image above, a square with four 5-cm sides and four 90 ° angles is shown.
6- The area of a square
The area of a square is equal to the product of one side and 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, that is (side) 2.
Some examples of calculating the area of a square are:
- Square with 2 m sides: 2 mx 2 m = 4 m 2
- Squares with 52 cm sides: 52 cm x 52 cm = 2704 cm 2
- Square with 10mm sides: 10mm x 10mm = 100mm 2
7- Squares are parallelograms
Parallelograms are a type of quadrilateral that have two pairs of parallel sides. This means that one pair of sides faces each other, while the same is true for the other pair.
There are four types of parallelograms: rectangles, rhombuses, rhomboids, and squares.
8- The opposite angles are congruent and the consecutive ones are complementary
That two angles are congruent means that they have the same amplitude. In this sense, since a square has all the angles of the same amplitude, it can be said that the opposite angles are congruent.
For its part, the fact that two consecutive angles are complementary means that the sum of these two is equal to a straight angle (the one that has an amplitude of 180 °).
The angles of a square are right angles (90 °), so their sum is 180 °.
9- They are built from a circumference
To construct a square, a circle is drawn. Subsequently, we proceed 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 intersect the circumference. If these four points are joined, the result is a square.
10- The diagonals intersect at their midpoint
Diagonals are straight lines that are drawn from one angle to another that is opposite. In a square, two diagonals can be drawn. 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 intersect 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.