How to Find the Orthocenter of a Triangle

How to construct draw a triangle given one side and the angle at each end of it with compass and straightedge or ruler. The incenter of a triangle has various properties let us look at the below image and state the properties one-by-one.

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As noted below there are four possible triangles that be drawn - they are all correct.

. It works by first copying the line segment to form one side of the triangle then copy the two angles on to each end of it to complete the triangle. The triangles AEI and AGI are congruent triangles by RHS rule of congruency. See Orthocenter of a triangle.

If I is the incenter of the triangle then line segments AE and AG CG and CF BF and BE are equal in length. It works using the construction for a perpendicular through a point to draw two of the altitudes thus location the orthocenter. Note If you find you cannot draw the arcs in steps 2 and 3 the orthocenter lies outside the triangle.

There are therefore three altitudes in a triangle. AI AI common in both triangles.

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