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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.
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How do you find orthocenter?
You find the orthocenter by constructing the altitudes from the vertices in a triangle. If the triangle is obtuse, the orthocenter will fall outside the triangle. If the triangle is acute, the orthocenter will fall on the inside of the triangle. If the triangle is a right triangle, the orthocenter will lie on a vertix.
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 intersection of the three altitudes of a triangle?
orthocenter
What is the use of a orthocenter?
The orthocenter is the point of concurrency of the altitudes in a triangle. A point of concurrency is the intersection of 3 or more lines, rays, segments or planes. The orthocenter is just one point of concurrency in a triangle. The others are the incenter, the circumcenter and the centroid.My daughter's math teacher recommended the following site, which was enormously helpful for her. Here's a link to the 'orthocenter' topic, and you can find a bunch of other math topic videos there. It is all free. Hope it will help.http://www.brightstorm.com/d/math/s/geometry/u/constructions/t/constructing-the-orthocenter
What is a real word application of the orthocenter?
Ah, the orthocenter is a special point where the altitudes of a triangle intersect. In real life, architects and engineers use the concept of the orthocenter when designing structures like bridges or roofs. By understanding how the altitudes intersect at the orthocenter, they can create stable and balanced designs that can withstand different forces. It's like adding a touch of harmony and balance to their creations, creating a strong foundation just like the base of a happy little tree.
How do you find orthocenter?
You find the orthocenter by constructing the altitudes from the vertices in a triangle. If the triangle is obtuse, the orthocenter will fall outside the triangle. If the triangle is acute, the orthocenter will fall on the inside of the triangle. If the triangle is a right triangle, the orthocenter will lie on a vertix.
Where is the orthocenter on an obtuse triangle?
An orthocenter on an obtuse triangle actually lies outside of the triangle. In an acute triangle, the orthocenter lies within the triangle.
The orthocenter of a triangle may lie outside the triangle since?
The orthocenter is the point where the altitudes of a triangle intersect. An orthocenter lies outside of a triangle only when the triangle is obtuse. If a triangle is acute, the orthocenter lies inside of the triangle.
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.
If a triangle is obtuse where is the orthocenter of the triangle found?
If a triangle is obtuse, the orthocenter of the triangle actually lies outside of the triangle. If the triangle is acute, the orthocenter of the triangle lies on the inside of the triangle
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.
The intersection of the altitudes of a triangle..?
ORTHOCENTER
What are the properties the orthocenter of a triangle?
Construct a scalene triangle and then from each of its vertices draw a straight line that is perpendicular to its opposite side and where these 3 straight lines intersect it is the orthocenter of the triangle. The position of the orthocenter can vary depending on what type of triangle it.
The orthocenter is the point shared by the angle bisector of a triangle?
Actually, the orthocenter of a triangle is the point where the three altitudes of the triangle intersect. The altitudes are perpendicular lines drawn from each vertex to the opposite side. The angle bisectors of a triangle intersect at the incenter, not the orthocenter.
The intersection of the altitudes of a triangle is called?
orthocenter
What is the intersection of the three altitudes of a triangle?
orthocenter
Which is the point of concurrency of the altitudes of a triangle?
orthocenter
