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Name all types of triangles for which the centroid circumcenter incenter and orthocenter are all inside the triangleand classify the triangles according to the sides as well as the angles?
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∙ 14y ago
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∙ 14y ago
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Name the 4 points of concurrence in triangles?
When three or more lines intersect at one point, then they are considered concurrent.The four points of concurrence in triangles are the circumcenter, incenter, centroid, and orthocenter.
What is the intersection of 3 altitudes of triangles?
its called the orthocenter
Why is there a orthocenter?
There just is :)In all seriousness, all triangles (by definition) have an orthocenter and other points of concurrency. The definitions of an orthocenter is the place where the altitudes of all three sides intersect.
What is the name of the point at which all triangles altitudes converge?
orthocenter
What is the purpose of an orthocenter?
In short, the orthocenter really has no purpose. There are 4 points of Concurrency in Triangles: 1) The Centroid - the point of concurrency where the 3 medians of a triangle meet. This point is also the triangle's center of gravity. 2) The Circumcenter - the point of concurrency where the perpendicular bisectors of all three sides of the triangle meet. This point is the center of the triangle's circumscribed circle. 3) The Incenter - the point of concurrency where the angle bisectors of all three angles of the triangle meet. Like the circumcenter, the incenter is the center of the inscribed circle of a triangle. 4) The Orthocenter - the point of concurrency where the 3 altitudes of a triangle meet. Unlike the other three points of concurrency, the orthocenter is only there to show that altitudes are concurrent. Thus, bringing me back to the initial statement.
What is the name of the point at which all of a triangles perpendicular bisectors intersect?
It's the circumcenter.
What type of triangle has its orthocenter outside of the triangle?
The orthocenter of a triangle is found at the intersection of the three altitudes of the triangle. Obtuse triangles contain altitudes which are found outside of the triangle, meaning their orthocenter must be outside of the triangle as well.
What is an orthocentre and where it is located for an obtuse right and a right angled triangles?
On an obtuse triangle the orthocenter is located on the outside of the triangle and the orthocenter of the right triangle is located at the vertex of the triangle ...
When is the circumcenter of a triangle in the exterior of the triangle?
All triangles with an obtuse angle will have the circumcentre outside the boundary of the triangle.
When does a triangles circumcenter fall outside of the triangle?
A triangle with one angle bigger than 90 degrees will have its circumscribing circle's centre outside that triangle.
What are the properties of an equilateral triangle?
Equilateral triangles have, by definition, 3 equal sides. This means they also have 3 equal angles (i.e. they are equiangular) with each angle measuring 60 degrees. They have 3 lines of symmetry from each vertex to the midpoint of the opposite side. These lines are the medians, perpendicular bisectors, altitudes, and angle bisectors of the triangle. The point where these three lines intersect is the centroid, incenter, circumcenter, and orthocenter of the triangle. The area of an equilateral triangle is sqrt(3)/4*s where s is the side length of the triangle.
Name all types of triangles for which the point of concurrency is inside the triangle?
The answer depends on what point of concurrency you are referring to. There are four segments you could be talking about in triangles. They intersect in different places in different triangles. Medians--segments from a vertex to the midpoint of the opposite side. In acute, right and obtuse triangles, the point of concurrency of the medians (centroid) is inside the triangle. Altitudes--perpendicular segments from a vertex to a line containing the opposite side. In an acute triangle, the point of concurrency of the altitudes (orthocenter) is inside the triangle, in a right triangle it is on the triangle and in an obtuse triangle it is outside the triangle. Perpendicular bisectors of sides--segments perpendicular to each side of the triangle that bisect each side. In an acute triangle, the point of concurrency of the perpendicular bisectors (circumcenter) is inside the triangle, in a right triangle it is on the triangle and in an obtuse triangle it is outside the triangle. Angle bisectors--segments from a vertex to the opposite side that bisect the angles at the vertices. In acute, right and obtuse triangles, the point of concurrency of the angle bisectors (incenter) is inside the triangle.
