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Is the orthocenter of a triangle always inside the triangle?
A Triangle's OrthocenterNo, it can be outside the triangle.
Will the incenter of a triangle always be located inside of the triangle?
Yes, it will.
Which statement about an altitude of a triangle is always true?
Well, isn't that a happy little question! The altitude of a triangle is always perpendicular to the base it intersects. It's like a little friend that helps the triangle stand tall and proud. Just remember, in the world of triangles, altitudes are always there to lend a hand and make everything more balanced and beautiful.
When is the orthocenter inside on or outside of the triangle?
Inside: acute angled triangleOn: right angled triangle Outside: obtuse angled triangle.
Is centroid of a triangle located inside the triangle?
Yes
Will the medians always intersect inside an acute triangle?
Yes.
Will medians sometimes intersect inside a acute triangle?
Always.
Are the medians always inside a right triangle?
no
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.
Do angle bisectors always intersect inside the triangle?
Yes.
A median of a triangle may fall outside the triangle?
A median of a triangle is a line segment joining the vertex to the midpoint of the opposite side. The medians ( each triangle has 3) always intersect at a point call the centroid and the centroid is always INSIDE the triangle.APEX: The incenter of a triangle ________ falls outside of its triangle. = neverA median of a triangle may fall outside the triangle? false apex!!!!!!!!
What is the fewest number of medians that lie within a triangle?
All three medians MUST lie inside the triangle.
Where is the centroid located in an acute triangle?
Where the medians meet, inside the triangle.
Does the altitude of a triangle always intersect inside the triangle?
No. Not if the triangle is right angled (the intersection is AT the right vertex) or obtuse angled (intersection outside).
Which type of triangle contains its centroid?
All types of triangles—scalene, isosceles, and equilateral—contain their centroid. The centroid, which is the point where the three medians intersect, is always located inside the triangle, regardless of its type. This property holds true because the centroid is calculated as the average of the vertices' coordinates, ensuring it lies within the triangle's boundaries.
Which two points of concurrency always remain inside the triangle and why?
The two points of concurrency that always remain inside a triangle are the centroid and the incenter. The centroid, formed by the intersection of the medians, is the triangle's center of mass and always lies within the triangle. The incenter, formed by the intersection of the angle bisectors, is equidistant from all sides and, by the properties of triangles, must also be located inside the triangle.
