Geogebra - Orthocenter

This post is a step by step guide to constructing the orthocenter of a triangle in Geogebra - an online graphing calculator. So let’s get going straight away. 

Orthocenter is the point where the three altitudes of a triangle intersect. So all we have to do really is draw altitudes of a triangle, and mark the location where they intersect with a dot(point). 

We begin by constructing any casual triangle using the Polygon tool. If you want to know how to construct a specific triangle from three known side lengths or two known side lengths & one given angle, check out this post of mine. 

Step 1 : Select Polygon tool by a simple left mouse click or a single tap on screen. This tool is found in the Polygons section of the shapes menu. 

After selecting this tool, in the graphing panel on the right, click on three different spots to mark the location of three vertices of your triangle. Click on the first point you marked again to complete the construction of a triangle. 

Step 2 : If your triangle is an obtuse angled triangle like mine in the picture, then you would need to extend the three sides beyond the limits of the triangle. Select the Line tool under the Lines section. 

Click on the vertices A and B to draw a line containing the side AB. Similarly, click on the pairs of vertices B & C and A & C to draw lines containing the sides BC and AC. 

Step 3 : Constructing the altitudes. Select the tool Perpendicular Line in the Construct section. 

To draw an altitude, click on a vertex first and then the side opposite to the vertex(or the line containing the opposite side). Similarly, construct the other two altitudes.

So the spot where the three altitudes are intersecting is where the Orthocenter is located. 

Step 4 : Mark this location with a dot(point). Select the Intersect tool under the Basic Tools section, click on any of the two altitudes. 

Click on any pair of altitudes. The point(dot) will appear at the spot where they are intersecting. In the above figure, point D is the Orthocenter, and it is outside the triangle because the triangle is an obtuse triangle.