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What triangle is the point of concurrency of the angle bisectors of a triangle?
circumcenter circumcenter is wrong, it is the incenterbecause the point of concurrency is always on the inside of the triangle.
Is it true that the point of concurrency of any triangle only happens inside the triangle?
Depends on the point of concurrency of what. The point of concurrency of altitudes will be outside in any obtuse triangle.
Can an angle bisector of a triangle always intersect inside the triangle?
The angle bisectors always intersect inside the triangle. (This is not true for altitudes and right bisectors.)
Do the three altitudes of an obtuse triangle always intersect inside the triangle?
No.
Where is the centroid located in an acute triangle?
Where the medians meet, inside the triangle.
What triangle is the point of concurrency of the angle bisectors of a triangle?
circumcenter circumcenter is wrong, it is the incenterbecause the point of concurrency is always on the inside of the triangle.
Is it true that the point of concurrency of any triangle only happens inside the triangle?
Depends on the point of concurrency of what. The point of concurrency of altitudes will be outside in any obtuse triangle.
Point of concurrency of any triangle only happens inside of a triangle?
yes
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.
Will the incenter of a triangle always be located inside of the triangle?
Yes, it will.
Do the altidudes of a triangle always meet in the interior of the triangle?
In a obtuse triangle, the point of concurrency, where multiple lines meet, of the altitudes, called the orthocenter, is outside the triangle. In a right angle, the orthocenter lies on the vertex (corner) of the right angle. In an acute angle, the orthocenter lies inside the triangle.
Is the orthocenter of a triangle always inside the triangle?
A Triangle's OrthocenterNo, it can be outside the triangle.
Is centroid of a triangle located inside the triangle?
Yes
Can an angle bisector of a triangle always intersect inside the triangle?
The angle bisectors always intersect inside the triangle. (This is not true for altitudes and right bisectors.)
Do the medians of a triangle always intersect inside the triangle?
Yes.
Do the three altitudes of an obtuse triangle always intersect inside the triangle?
No.
Where is the centroid located in an acute triangle?
Where the medians meet, inside the triangle.
