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Hello, good morning. In today's class we are going to continue with the subject of polygons and we are going to deal with the simplest polygon, which are the triangles.

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We are going to see what a triangle is, the elements that make it up, and other important elements of the triangles.

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But let's start the explanation with a question I have for you.

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What are the most used triangles in technical drawing?

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Rectangular triangles, isosceles triangles, I don't know if you remember these courses, but I have an answer to this question.

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The most important triangles in technical drawing are these two, the square and the arch.

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We start with the definition of triangle.

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A triangle is a three-dimensional polygons.

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To the sides, we call the segments that form the polygon, we call them sides, and to the points where the sides are built, we call them vertices.

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A triangle has no diagonal. And very important, how do we call each vertex, each side?

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has a specific name. The vertex is called, the notation of a capital letter is used, A, B and C and on the sides we use the same

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letters in lowercase to name the opposite side. This is always used in mathematics. If this is the

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vertex B, the opposite side is the side B. If this is the vertex A, the opposite side is the vertex A.

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Next aspect, what is the classification of the triangles according to the sides, we have

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if the three sides are equal, 0 is a triangle, if the two sides are equal and one

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different, we have an austere triangle and if the three sides are different, we have

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the scale. We can also classify the triangles according to their angles. If their three angles

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are acute angles, that is, less than 90 degrees, then it is an octagonal triangle. If one of

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the angles appears is straight, that is, 90 degrees, in this case an angle A is 90 degrees,

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triangle the rectangle and if one of the sides is obtuse, that is, greater than 90 degrees, then we have an obtuse triangle.

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Observe that in an obtuse triangle there are two acute angles, the same in the rectangle.

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In fact, how do we classify a triangle with its angles?

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to see if a straight line appears or if it appears in this video you can see more about this

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good lines important of the triangles we are going to see the mediatrixes are the mediatrixes

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of the sides of the triangle they have already seen that a mediatrix is a straight line that cuts

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perpendicular to a segment on each side if we draw the mediators these are

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important effects we have the bisectrices equally from each angle we can

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draw the bisectrix we have three bisectrices in a medium triangle

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they are segments that join the vertices with the middle points on the opposite side this is a

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We join the vertex with the middle point on the opposite side, and finally we have the heights, which are perpendicular segments to the sides, drawn from the vertex to the opposite side.

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From the B vertex, we draw a perpendicular to the opposite side, and this will be the height in B.

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of course from these important lines we have the points of

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competition that this is the most important

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of a triangle that happens when there are some points that are special in the triangle

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the center circle is where the mediators are cut and it is also the center of the

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circumference written to the triangle. If I want to make a triangle that passes through the three vertices of the

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the triangle, I will have to determine the circumference, that is its center.

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On the other hand, I have the in-center. The in-center is the point where the three bisectrices of the triangle are cut,

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and it is also the center of the unscripted circumference.

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This circumference that is tangent to the triangle.

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Another important point is the barycenter.

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It is the center of gravity of the triangle, that is, if we suspended it from this

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varicenter, it would remain horizontal. Imagine that we hang a triangle with a thread just

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stuck to the triangle from the varicenter, this would remain horizontal because it is its center of gravity.

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The varicenter is the point where the three medians are cut. And finally we have the

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center, which is where the three circles are. Well, I hope it has been clear to you what a triangle is

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and what are the most important elements of it. Thank you very much and do not stop working. Greetings!