The triangle in which the orthocenter lie on the perimeter of the triangle is:
Right Triangle.
Orthocenter of a triangle--
The orthocenter of a triangle is a point where the three altitudes of a triangle intersect.
As we know that in a right angled triangle each leg of the triangle act as an altitude.
Hence, in a right triangle the vertex containing the right angle will behave as the orthocenter of the triangle and hence lie on the perimeter of the triangle.
Hence, the answer is:
Right triangle.
In right angle triangle the orthocenter is on the perimeter of the triangle.
Further explanation:
An altitude is a line that is perpendicular to a side and passes through opposite vertex.
The point at which all the three altitudes of a triangle intersect each is known as orthocenter of the triangle.
Orthocenter of a triangle lies inside the triangle if it is acute.
Orthocenter of a triangle lies on the vertex of the triangle that is opposite to hypotenuse if it is right angled.
Orthocenter of a triangle lies outside the triangle if it is obtuse.
An orthocenter is the point at which all the three altitudes of the triangle intersect each other.
In right angle triangle the orthocenter is on the perimeter of the triangle.
Kindly refer to the image attached.
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangles
Keywords: orthocenter, perimeter, triangle, right angle triangle, perpendicular, altitudes, point, triangle, intersect, centroid, circumcenter, bisectors, perpendicular bisectors, angles,angle bisectors, median, intersection, incenter, right angle triangle, equilateral triangle, obtuse, acute.
