Centroids and Orthocenters

Centroid of a triangle
The median of a triangle connects a vertex with the midpoint of the opposite side.[br][br]In the triangle below: [br]1) use the point tool to create the midpoint of each side of the triangle;[br]2) use the line tool to create a [b]segment[/b] connecting each midpoint with the opposite vertex.[br][br]The points where the medians intersect is the centroid of the triangle.[br][br]Use the move tool (the arrow), to move one of the vertices.[br]Note the location of the centroid when the triangle is:[br]4) acute;[br]5) obtuse;[br]6) right-angled.
Are the medians concurrent?
If the triangle is acute, where is the centroid?
If the triangle is obtuse, where is the centoid?
If the triangle is a right-angled triangle, where is the centroid?
Orthocenter
The altitude of a triangle is the segment perpendicular to one side of a triangle to the opposite vertex.[br][br]In the triangle below use the perpendicular line tool to:[br]1) create a perpendicular to side [i]AB[/i] through [i]C [/i](select the perpendicular tool, then select side [i]AB[/i], then [i]C[/i])[i];[br][/i]2) create a perpendicular to side [i]AC[/i] through [i]B;[/i][br]3) create a perpendicular to side [i]BC[/i] through [i]A[/i].[br][br]The points where the altitudes intersect is the orthocenter of the triangle.[br][br]Use the move tool (the arrow), to move one of the vertices.[br]Note the location of the orthocenter when the triangle is:[br]4) acute;[br]5) obtuse;[br]6) right-angled.[br][br]
Are the altitudes concurrent?
If the triangle is acute, where is the orthocenter?
If the triangle is obtuse, where is the orthocenter?
If the triangle is a right-angled triangle, where is the orthocenter?
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Information: Centroids and Orthocenters