Definition of rectangle triangle - What is it, Meaning and Concept

The triangles are polygons that have three sides .Remember that the polygons are flat figures, delimited by segments (i.e.on its sides).The triangle, therefore, is a flat figure formed by three segments.

When a triangle has a right angle (measuring ninety degrees), it is classified as a right triangle .The other two angles of the right triangle are always sharp (less than ninety degrees).

The right angle in the rectangular triangle is formed by the two sides of smaller length, known as legs , while the third side (the one of greater extension) receives the name of hypotenuse .The properties of these triangles indicate that the length of the hypotenuse is always less than the sum of the legs.The hypotenuse, on the other hand, is always longer than either of the two legs.

The famous Pitagoras theorem is based on these characteristics of the rectangular triangles and indicates that the square of the hypotenuse is identical to the result of the sum of the squares of the two legs.

In this way, the following equation is established for every right triangle:

Hypotenuse squared=Squared leg + Squared leg

It should be noted that the rectangular triangles can be isosceles triangles (the two legs have the same extension: that is, they are equal) or scalene triangles (the extension of each side is different from the remaining two).

On the other hand, if we want to calculate the area of a right triangle, we can appeal to the following formula:

Area=(Cathet x Cathetus)/2

As you can see, one of the fundamental points of the triangles is the relationships that we can establish between their different sides and angles, something that is essential to solve a large number of problems, both in the field of mathematics as in many others.Before continuing with these relationships, it is necessary to cover another topic: the orthogonal projection .

The orthogonal projection belongs to the scope of the Euclidean geometry , which studies the geometric properties of the spaces in which the axioms of Euclid, a group of propositions considered obvious that others can generate through logical deductions.To make an orthogonal projection two elements are necessary: ​​ a set of points (which can be composed of only one); a projection line .The first is projected onto the line with the help of auxiliary lines perpendicular to it, so that the resulting dimensions are only correct in one case: when a segment parallel to the line is projected.

This concept is often used in the development of video games to create a false sense of depth, since the distance of objects with respect to the camera does not matter: always they will have the same dimensions on the screen.Now, if we project the legs on the hypotenuse in this way, we obtain a geometric mean called height relative to the hypotenuse , a segment that starts from the point where they are both legs and cut the hypotenuse perpendicularly.

When we trace the height relative to the hypotenuse, the rectangular triangle becomes three triangles: the original plus the two that it contains (as seen in the image).This gives rise to certain relationships For example, the sum of both projections is equal to the hypotenuse ( a=m + n ).It is also correct to say that the product of the two projections is equal to the square of the hypotenuse, since that h/m=n/h , and if we clear h it gives us hh=mn .

The product between the projection of a leg and the hypotenuse is equal to the square of that leg: b/a=m/b=> bb=am .Lastly, the product of the legs is equal to the relative height multiplied by the hypotenuse: a/c=b/h=> ah=bc .