Hello to all! In this post, we looked at a simple geometric shape – an angle, got acquainted with the types of angles, and learned about the basic properties of this figure, as well as the methods of their notation. Today we will find out what basic shapes can come from several angles (polygons). And let’s start with the triangle.

So, a triangle – as the name implies – a geometric figure consisting of three (:)) angles (which are the vertices of the triangle) and three sides:

The most important feature of a triangle is the fact that the sum of the angles of a triangle is always 180 ° (example in the pictures below):

As you can see from the pictures – the sum of the angles of each of the triangles is 180 degrees – no matter what triangle we create.

In the text, a triangle is denoted by the sign Δ and three capital Latin letters that indicate the vertices of the triangle. For example, in the figure below we have a triangle ABC (ΔABC) with sides a, b, c:

As for the types of triangles, there are only three of them:

– rectangular (two angles of sharp (less than 90 °), and one corner of the line (equal to 90 °):

– acute-angled (each of the three angles is less than 90 °):

– obtuse (one angle is greater than 90 °, the other two are less than 90 °):

With the triangles and their views, we are done. Now let’s ask ourselves the question: what will happen if the figure has four sides and vertices, not four? Let’s start with the square. A strict scientific explanation of the square is as follows: a square is a rectangle in which all sides are equal.

In simple terms, a square is a figure with four vertices, and the length of all sides is equal. The essence is the same, but it sounds, as for me – easier, and not so dry. But it’s up to you to decide 🙂

In the text, the square is denoted in capital Latin letters denoting the vertices of the square. For example, in the figure below we have the square ABCD:

It should be noted that the square consists of four corners: BAD, ABC, BCD, CDA. As for the sides of the square, they (sides: a, b, c, d) are completely equal:

And what will happen if the square does not have all sides equal? It turns out that if not all sides are equal in the square, but only the opposite, and the angles are 90 ° – then this will not be a square, but a rectangle. The rectangle in the text is denoted in the same way as the square – in capital Latin letters. In the figure below – a rectangle ABCD (capital letters indicate the vertices of the rectangle), with sides a, b, c, d – and, as can be seen from the figure, the opposite sides are equal to each other: side a = side c, and side b = side d:

Ok … we figured out the rectangle … and move on to the polygons: geometric shapes of various shapes, which, like triangles, squares and rectangles, consist of sides (the segments that make up the polygon) and vertices (points at which the sides intersect). In the figure below – the polygon ABCDEFG (by the way, the polygon in the text is denoted similarly with a triangle / square / rectangle – in capital Latin letters), consisting of the vertices and sides a, b, c, d, e, f, g:

That’s all for now 🙂 In the next entry on the basics of geometry, we’ll talk about a circle and a circle. It will be interesting!