In a right triangle, the altitude from each acute angle coincides with a leg and intersects the opposite side at (has its foot at) the right-angled vertex, which is the orthocenter. The altitudes from each of the acute angles of
an obtuse triangle
lie entirely outside the triangle, as does the orthocenter H.
In which triangle do the three altitudes intersect outside?
It turns out that all three altitudes always intersect at the same point – the so-called
orthocenter of the triangle
. The orthocenter is not always inside the triangle. If the triangle is obtuse, it will be outside.
What type of triangle has 3 altitudes?
For
any acute triangle
, the three altitudes of the triangle intersect a vertex and opposite side of the triangle. Therefore, for an acute triangle the orthocenter will always be on the interior of the triangle.
What special triangle whose intersection of its three altitudes is exactly on one of its vertices?
When all three altitudes are drawn on the same triangle, they intersect at exactly one point,
the orthocenter
.
Which point is the intersection of the altitude of a triangle?
The orthocenter
is the point of intersection of the altitudes of the triangle, that is, the perpendicular lines between each vertex and the opposite side. When the orthocenter is combined with the three vertices, any one of the points is the orthocenter of the other three.
What is Orthocentre formula?
Orthocenter Formula. The word “ortho” stands for “right.” The orthocenter formula represents
the center of all the right angles
. It is drawn from the vertices to the opposite sides i.e., the altitudes.
What is the Orthocentre of triangle?
An orthocenter can be defined as the point of intersection of altitudes that are drawn perpendicular from the vertex to the opposite sides of a triangle. The orthocenter of a triangle is that
point where all the three altitudes of a triangle intersect
.
What is the longest altitude of a triangle?
Thus, the longest altitude is
perpendicular to the shortest side of the triangle
. The altitudes are also related to the sides of the triangle through the trigonometric functions.
What is the difference between altitude and height of a triangle?
The altitude of a triangle is the
perpendicular line segment drawn from the vertex of the triangle to the side opposite to it
. The altitude makes a right angle with the base of the triangle that it touches. It is commonly referred to as the height of a triangle and is denoted by the letter ‘h’.
Which two triangle centers are always inside the triangle?
Like the centroid,
the incenter
is always inside the triangle.
What is the shortest side of a 30 60 90 triangle?
Because it is a special triangle, it also has side length values which are always in a consistent relationship with one another. And so on.
The side opposite the 30° angle is always the smallest
, because 30 degrees is the smallest angle.
What is the segment of a triangle?
A midsegment of a triangle is a segment that
connects the midpoints of two sides of a triangle
. In the figure D is the midpoint of ̄AB and E is the midpoint of ̄AC .
Is equidistant from the vertices of a triangle?
The circumcenter
of a triangle is a point that is equidistant from all three vertices.
Where does the altitude of a triangle lie?
An altitude of a triangle is the
perpendicular segment from a vertex of a triangle to the opposite side (or the line containing the opposite side)
. An altitude of a triangle can be a side or may lie outside the triangle.
Where do medians intersect triangles?
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at
the triangle’s centroid
.
Can orthocenter lies outside triangle?
For an acute angle triangle, the orthocenter lies inside the triangle. For
the obtuse angle triangle
, the orthocenter lies outside the triangle. For a right triangle, the orthocenter lies on the vertex of the right angle.
