We can construct it using a ruler and aĬompass as described in the lesson How to draw a parallel line In the topic Angles, complementary, supplementary angles of Such a lineĭoes exist due to postulate 1 of the lesson Parallel lines The point C parallel to the triangle side AB. Let us draw (construct) the straight line GH passing through We need to prove that altitudes AD, BE and CF intersect Points of the altitudes and the opposite triangle sides. The points D, E and F are the intersection Three altitudes of a triangle are concurrent, in other words, they intersect at one point.įigure 1 shows the triangle ABC with the altitudes AD, BE and CFĭrawn from the vertices A, B and C to the opposite sides BC, ACĪnd AB respectively. So, I suppose you are familiar with the contents of these lessons. I will refer also to the lessons Properties of the sides of parallelograms and How to draw a parallel line passing through a given point using a compass and a ruler under the current topic Triangles of the section Geometry in this site, as well as to the lesson Parallel lines under the topic Angles, complementary, supplementary angles of the section Geometry in this site. The proof is based on the perpendicular bisector properties that were proved in the lesson Perpendicular bisectors of a triangle sides are concurrent under the current topic Triangles of the section Geometry in this site. The altitudes possess a remarkable property: all three intersect at one point. In this lesson we consider the altitudes of a triangle.
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