Trace the heights of a triangle and its orthocenter determine there are three heights which can be drawn in a triangle. What are the properties of these straight lines and what is the orthocenter of a triangle? I. the heights of a triangle a triangle height is the straight line that passing through a vertex falls perpendicularly on the side opposite to the vertex. Building height that passes through A vertex of the triangle means to construct a line perpendicular to the side BC, passing through a. Notes: in Figure 1, point A is called the height base that comes out of the word. height indicates the line that joins the vertex with the base (the segment AA of Figure 1).
The word height also means the length of the segment (length AA of Figure 1). This is the meaning intended when we say that the area of a triangle is equal to a half productdata of the base by the height. II. the orthocenter of a triangle 1. Property in a triangle, three heights are concurrent.
Their point of intersection is called orthocenter of the triangle. In Figure 3, the H-point is the orthocenter of the triangle. Note: in practice, we need only draw two heights to obtain the orthocenter of a triangle. 2 Position the orthocenter of the orthocenter is not always located in the interior of the triangle. We can observe that: If the three angles of the triangle are acute, the orthocenter is inside the triangle (first case). If the triangle is one obtuse angle (greater than a right angle), the orthocenter will be outside the triangle – will be outside the triangle-(second case). If the triangle is of type rectangle, then the orthocenter is situated at the apex of the right angle (third case). Note: given the triangle and taking its orthocenter H, we can observe C is the orthocenter of the triangle. For the same reason, the orthocenter of the triangle would be A vertex, and the orthocenter of would be B.