Example Worksheet: Orthocenter of a Triangle

Below you can see a triangle [i]ABC[/i] together with its heights. [br]The intersection point of the three heights is called [color=#ff0000]orthocenter[/color] of the triangle.[br][br]Modify the dynamic construction in order to examine the orthocenter of different triangles and explore the properties of the orthocenter.
Task 1
How do you construct the [color=#ff0000]orthocenter [/color]of a triangle? Write down detailed construction steps.[br][u]Hint[/u]: You can use the arrow buttons of the [i]Navigation Bar[/i] in order to redo the construction.
Task 2
You can modify the shape of the triangle by dragging its [color=#0000ff]vertices [/color]with the mouse. Therby, the [color=#ff0000]orthocenter [/color]and [color=#38761d]angles [/color]change too.[br]Try to describe the position of the [color=#ff0000]orthocenter[/color] when..[br] a) all angles are acute.[br] b) one angle is obtuse.[br] c) one angle is a right angle.

Information: Example Worksheet: Orthocenter of a Triangle