Changes
From Karnataka Open Educational Resources
1,497 bytes removed
, 01:29, 6 December 2013
| Line 170: |
Line 170: |
| | # Is it possible to construct a triangle with 3 collinear points? | | # Is it possible to construct a triangle with 3 collinear points? |
| | # Is it possible to construct a triangle whose sides are 3cm, 4cm and 9cm. Give reason. | | # Is it possible to construct a triangle whose sides are 3cm, 4cm and 9cm. Give reason. |
| − |
| |
| − |
| |
| − | == Summary of triangle centres ==
| |
| − |
| |
| − | There are many types of
| |
| − | triangle centers. Below are four of the most common.
| |
| − |
| |
| − |
| |
| − | {| border="1"
| |
| − | |-
| |
| − | |
| |
| − | Incenter
| |
| − |
| |
| − |
| |
| − | |
| |
| − | [[Image:KOER%20Triangles_html_ef07362.gif]]
| |
| − |
| |
| − |
| |
| − | |
| |
| − | Located at intersection of the angle bisectors.
| |
| − | See Triangle
| |
| − | incenter definition
| |
| − |
| |
| − |
| |
| − | |-
| |
| − | |
| |
| − | Circumcenter
| |
| − |
| |
| − |
| |
| − | |
| |
| − | [[Image:KOER%20Triangles_html_68b61322.gif]]
| |
| − |
| |
| − |
| |
| − | |
| |
| − | Located at intersection of the perpendicular bisectors of the
| |
| − | sides.
| |
| − | See Triangle circumcenter definition
| |
| − |
| |
| − |
| |
| − | |-
| |
| − | |
| |
| − | Centroid
| |
| − |
| |
| − |
| |
| − | |
| |
| − | [[Image:KOER%20Triangles_html_16723946.gif]]
| |
| − |
| |
| − |
| |
| − | |
| |
| − | Located at intersection of medians.
| |
| − | See Centroid of a
| |
| − | triangle
| |
| − |
| |
| − |
| |
| − | |-
| |
| − | |
| |
| − | Orthocenter
| |
| − |
| |
| − |
| |
| − | |
| |
| − | [[Image:KOER%20Triangles_html_7aa50a01.gif]]
| |
| − |
| |
| − |
| |
| − | |
| |
| − | Located at intersection of the altitudes of the triangle.
| |
| − | See
| |
| − | Orthocenter of a triangle
| |
| − |
| |
| − |
| |
| − | |}
| |
| − | In the case of an equilateral triangle, all four
| |
| − | of the above centers occur at the same point.
| |
| − |
| |
| − |
| |
| − | The Incenter of a
| |
| − | triangle
| |
| − |
| |
| − |
| |
| − | Latin: in - "inside,
| |
| − | within" centrum - "center"
| |
| − |
| |
| − |
| |
| − | The point where the
| |
| − | three angle bisectors of a triangle meet.
| |
| − | One of a triangle's
| |
| − | points of concurrency.
| |
| − |
| |
| − |
| |
| − | Try this Drag the
| |
| − | orange dots on each vertex to reshape the triangle. Note the way the
| |
| − | three angle bisectors always meet at the incenter.
| |
| − |
| |
| − |
| |
| − |
| |
| − |
| |
| − |
| |
| − |
| |
| − | One of several centers the triangle can have, the
| |
| − | incenter is the point where the angle bisectors intersect. The
| |
| − | incenter is also the center of the triangle's incircle - the largest
| |
| − | circle that will fit inside the triangle.
| |
| | | | |
| | | | |
