[b]Step 1: [/b] Use [icon]https://www.geogebra.org/images/ggb/toolbar/mode_orthogonal.png[/icon] to construct the line through A and perpendicular to BC.[br][b]Step 2: [/b] Use [icon]https://www.geogebra.org/images/ggb/toolbar/mode_orthogonal.png[/icon]to construct the line through B and perpendicular to AC.[br][b]Step 3: [/b] Use [icon]https://www.geogebra.org/images/ggb/toolbar/mode_orthogonal.png[/icon] to construct the line through C and perpendicular to AB.[br][br][b][color=#cc0000]Each line you constructed above contains an altitude of the triangle.[/color][/b][br][b]Step 4[/b]: Use [icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon] to place a point where the altitudes intersect.[br][b]Step 5:[/b] Use [icon]/images/ggb/toolbar/mode_showhidelabel.png[/icon] to add a label to this point where the altitudes intersect.
[b][color=#cc0000]The point where all the altitudes intersect is called the orthocenter.[/color][/b][br][br]To answer the questions below, it might help to [icon]/images/ggb/toolbar/mode_angle.png[/icon]measure each angle of the original triangle ABC.
1. For what type of triangle is the orthocenter outside the triangle?
[size=100]2. Move your triangle around so that the orthocenter is on a vertex. What is true about the triangle when this happens?[/size]
3. Move your triangle so that vertex A is directly above on a vertical line from the orthocenter. What is true about the triangle when this happens?