Changes
From Karnataka Open Educational Resources
1,098 bytes removed
, 01:32, 6 December 2013
| Line 172: |
Line 172: |
| | | | |
| | | | |
| − | == Orthocenter of a Triangle ==
| |
| − |
| |
| − | From Greek: orthos -
| |
| − | "straight, true, correct, regular" The point where the
| |
| − | three altitudes of a triangle intersect. One of a triangle's points
| |
| − | of concurrency.
| |
| − |
| |
| − |
| |
| − | Try this Drag the
| |
| − | orange dots on any vertex to reshape the triangle. Notice the
| |
| − | location of the orthocenter.
| |
| − |
| |
| − |
| |
| − |
| |
| − |
| |
| − |
| |
| − | The altitude of a triangle (in the sense it used
| |
| − | here) is a line which passes through a vertex of the triangle and is
| |
| − | perpendicular to the opposite side. There are therefore three
| |
| − | altitudes possible, one from each vertex. See Altitude definition.
| |
| − |
| |
| − |
| |
| − | It turns out that all three altitudes always
| |
| − | intersect at the same point - the so-called orthocenter of the
| |
| − | triangle.
| |
| | | | |
| − |
| |
| − | The orthocenter is not always inside the triangle.
| |
| − | If the triangle is obtuse, it will be outside. To make this happen
| |
| − | the altitude lines have to be extended so they cross. Adjust the
| |
| − | figure above and create a triangle where the orthocenter is outside
| |
| − | the triangle. Follow each line and convince yourself that the three
| |
| − | altitudes, when extended the right way, do in fact intersect at the
| |
| − | orthocenter.
| |
| | | | |
| | | | |
| Line 325: |
Line 292: |
| | | | |
| | * Direct substitution | | * Direct substitution |
| − |
| |
| | | | |
| − |
| |
| − |
| |
| | == Evaluation == | | == Evaluation == |
| | | | |
